YES

We show the termination of the TRS R:

  active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
  active(__(X,nil())) -> mark(X)
  active(__(nil(),X)) -> mark(X)
  active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
  active(U12(tt(),V)) -> mark(U13(isNeList(V)))
  active(U13(tt())) -> mark(tt())
  active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
  active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
  active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
  active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
  active(U25(tt(),V2)) -> mark(U26(isList(V2)))
  active(U26(tt())) -> mark(tt())
  active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
  active(U32(tt(),V)) -> mark(U33(isQid(V)))
  active(U33(tt())) -> mark(tt())
  active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
  active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
  active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
  active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
  active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
  active(U46(tt())) -> mark(tt())
  active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
  active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
  active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
  active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
  active(U55(tt(),V2)) -> mark(U56(isList(V2)))
  active(U56(tt())) -> mark(tt())
  active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
  active(U62(tt(),V)) -> mark(U63(isQid(V)))
  active(U63(tt())) -> mark(tt())
  active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
  active(U72(tt(),P)) -> mark(U73(isPal(P),P))
  active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
  active(U74(tt())) -> mark(tt())
  active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
  active(U82(tt(),V)) -> mark(U83(isNePal(V)))
  active(U83(tt())) -> mark(tt())
  active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
  active(U92(tt())) -> mark(tt())
  active(isList(V)) -> mark(U11(isPalListKind(V),V))
  active(isList(nil())) -> mark(tt())
  active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
  active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
  active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
  active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
  active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
  active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
  active(isPal(V)) -> mark(U81(isPalListKind(V),V))
  active(isPal(nil())) -> mark(tt())
  active(isPalListKind(a())) -> mark(tt())
  active(isPalListKind(e())) -> mark(tt())
  active(isPalListKind(i())) -> mark(tt())
  active(isPalListKind(nil())) -> mark(tt())
  active(isPalListKind(o())) -> mark(tt())
  active(isPalListKind(u())) -> mark(tt())
  active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
  active(isQid(a())) -> mark(tt())
  active(isQid(e())) -> mark(tt())
  active(isQid(i())) -> mark(tt())
  active(isQid(o())) -> mark(tt())
  active(isQid(u())) -> mark(tt())
  active(__(X1,X2)) -> __(active(X1),X2)
  active(__(X1,X2)) -> __(X1,active(X2))
  active(U11(X1,X2)) -> U11(active(X1),X2)
  active(U12(X1,X2)) -> U12(active(X1),X2)
  active(U13(X)) -> U13(active(X))
  active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
  active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
  active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
  active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
  active(U25(X1,X2)) -> U25(active(X1),X2)
  active(U26(X)) -> U26(active(X))
  active(U31(X1,X2)) -> U31(active(X1),X2)
  active(U32(X1,X2)) -> U32(active(X1),X2)
  active(U33(X)) -> U33(active(X))
  active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
  active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
  active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
  active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
  active(U45(X1,X2)) -> U45(active(X1),X2)
  active(U46(X)) -> U46(active(X))
  active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
  active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
  active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
  active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
  active(U55(X1,X2)) -> U55(active(X1),X2)
  active(U56(X)) -> U56(active(X))
  active(U61(X1,X2)) -> U61(active(X1),X2)
  active(U62(X1,X2)) -> U62(active(X1),X2)
  active(U63(X)) -> U63(active(X))
  active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
  active(U72(X1,X2)) -> U72(active(X1),X2)
  active(U73(X1,X2)) -> U73(active(X1),X2)
  active(U74(X)) -> U74(active(X))
  active(U81(X1,X2)) -> U81(active(X1),X2)
  active(U82(X1,X2)) -> U82(active(X1),X2)
  active(U83(X)) -> U83(active(X))
  active(U91(X1,X2)) -> U91(active(X1),X2)
  active(U92(X)) -> U92(active(X))
  __(mark(X1),X2) -> mark(__(X1,X2))
  __(X1,mark(X2)) -> mark(__(X1,X2))
  U11(mark(X1),X2) -> mark(U11(X1,X2))
  U12(mark(X1),X2) -> mark(U12(X1,X2))
  U13(mark(X)) -> mark(U13(X))
  U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
  U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
  U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
  U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
  U25(mark(X1),X2) -> mark(U25(X1,X2))
  U26(mark(X)) -> mark(U26(X))
  U31(mark(X1),X2) -> mark(U31(X1,X2))
  U32(mark(X1),X2) -> mark(U32(X1,X2))
  U33(mark(X)) -> mark(U33(X))
  U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
  U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
  U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
  U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
  U45(mark(X1),X2) -> mark(U45(X1,X2))
  U46(mark(X)) -> mark(U46(X))
  U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
  U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
  U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
  U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
  U55(mark(X1),X2) -> mark(U55(X1,X2))
  U56(mark(X)) -> mark(U56(X))
  U61(mark(X1),X2) -> mark(U61(X1,X2))
  U62(mark(X1),X2) -> mark(U62(X1,X2))
  U63(mark(X)) -> mark(U63(X))
  U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
  U72(mark(X1),X2) -> mark(U72(X1,X2))
  U73(mark(X1),X2) -> mark(U73(X1,X2))
  U74(mark(X)) -> mark(U74(X))
  U81(mark(X1),X2) -> mark(U81(X1,X2))
  U82(mark(X1),X2) -> mark(U82(X1,X2))
  U83(mark(X)) -> mark(U83(X))
  U91(mark(X1),X2) -> mark(U91(X1,X2))
  U92(mark(X)) -> mark(U92(X))
  proper(__(X1,X2)) -> __(proper(X1),proper(X2))
  proper(nil()) -> ok(nil())
  proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
  proper(tt()) -> ok(tt())
  proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
  proper(isPalListKind(X)) -> isPalListKind(proper(X))
  proper(U13(X)) -> U13(proper(X))
  proper(isNeList(X)) -> isNeList(proper(X))
  proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
  proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
  proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
  proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
  proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
  proper(isList(X)) -> isList(proper(X))
  proper(U26(X)) -> U26(proper(X))
  proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
  proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
  proper(U33(X)) -> U33(proper(X))
  proper(isQid(X)) -> isQid(proper(X))
  proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
  proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
  proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
  proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
  proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
  proper(U46(X)) -> U46(proper(X))
  proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
  proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
  proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
  proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
  proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
  proper(U56(X)) -> U56(proper(X))
  proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
  proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
  proper(U63(X)) -> U63(proper(X))
  proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
  proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
  proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
  proper(isPal(X)) -> isPal(proper(X))
  proper(U74(X)) -> U74(proper(X))
  proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
  proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
  proper(U83(X)) -> U83(proper(X))
  proper(isNePal(X)) -> isNePal(proper(X))
  proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
  proper(U92(X)) -> U92(proper(X))
  proper(a()) -> ok(a())
  proper(e()) -> ok(e())
  proper(i()) -> ok(i())
  proper(o()) -> ok(o())
  proper(u()) -> ok(u())
  __(ok(X1),ok(X2)) -> ok(__(X1,X2))
  U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
  U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
  isPalListKind(ok(X)) -> ok(isPalListKind(X))
  U13(ok(X)) -> ok(U13(X))
  isNeList(ok(X)) -> ok(isNeList(X))
  U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
  U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
  U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
  U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
  U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
  isList(ok(X)) -> ok(isList(X))
  U26(ok(X)) -> ok(U26(X))
  U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
  U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
  U33(ok(X)) -> ok(U33(X))
  isQid(ok(X)) -> ok(isQid(X))
  U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
  U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
  U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
  U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
  U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
  U46(ok(X)) -> ok(U46(X))
  U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
  U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
  U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
  U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
  U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
  U56(ok(X)) -> ok(U56(X))
  U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
  U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
  U63(ok(X)) -> ok(U63(X))
  U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
  U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
  U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
  isPal(ok(X)) -> ok(isPal(X))
  U74(ok(X)) -> ok(U74(X))
  U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
  U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
  U83(ok(X)) -> ok(U83(X))
  isNePal(ok(X)) -> ok(isNePal(X))
  U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
  U92(ok(X)) -> ok(U92(X))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z))
p2: active#(__(__(X,Y),Z)) -> __#(Y,Z)
p3: active#(U11(tt(),V)) -> U12#(isPalListKind(V),V)
p4: active#(U11(tt(),V)) -> isPalListKind#(V)
p5: active#(U12(tt(),V)) -> U13#(isNeList(V))
p6: active#(U12(tt(),V)) -> isNeList#(V)
p7: active#(U21(tt(),V1,V2)) -> U22#(isPalListKind(V1),V1,V2)
p8: active#(U21(tt(),V1,V2)) -> isPalListKind#(V1)
p9: active#(U22(tt(),V1,V2)) -> U23#(isPalListKind(V2),V1,V2)
p10: active#(U22(tt(),V1,V2)) -> isPalListKind#(V2)
p11: active#(U23(tt(),V1,V2)) -> U24#(isPalListKind(V2),V1,V2)
p12: active#(U23(tt(),V1,V2)) -> isPalListKind#(V2)
p13: active#(U24(tt(),V1,V2)) -> U25#(isList(V1),V2)
p14: active#(U24(tt(),V1,V2)) -> isList#(V1)
p15: active#(U25(tt(),V2)) -> U26#(isList(V2))
p16: active#(U25(tt(),V2)) -> isList#(V2)
p17: active#(U31(tt(),V)) -> U32#(isPalListKind(V),V)
p18: active#(U31(tt(),V)) -> isPalListKind#(V)
p19: active#(U32(tt(),V)) -> U33#(isQid(V))
p20: active#(U32(tt(),V)) -> isQid#(V)
p21: active#(U41(tt(),V1,V2)) -> U42#(isPalListKind(V1),V1,V2)
p22: active#(U41(tt(),V1,V2)) -> isPalListKind#(V1)
p23: active#(U42(tt(),V1,V2)) -> U43#(isPalListKind(V2),V1,V2)
p24: active#(U42(tt(),V1,V2)) -> isPalListKind#(V2)
p25: active#(U43(tt(),V1,V2)) -> U44#(isPalListKind(V2),V1,V2)
p26: active#(U43(tt(),V1,V2)) -> isPalListKind#(V2)
p27: active#(U44(tt(),V1,V2)) -> U45#(isList(V1),V2)
p28: active#(U44(tt(),V1,V2)) -> isList#(V1)
p29: active#(U45(tt(),V2)) -> U46#(isNeList(V2))
p30: active#(U45(tt(),V2)) -> isNeList#(V2)
p31: active#(U51(tt(),V1,V2)) -> U52#(isPalListKind(V1),V1,V2)
p32: active#(U51(tt(),V1,V2)) -> isPalListKind#(V1)
p33: active#(U52(tt(),V1,V2)) -> U53#(isPalListKind(V2),V1,V2)
p34: active#(U52(tt(),V1,V2)) -> isPalListKind#(V2)
p35: active#(U53(tt(),V1,V2)) -> U54#(isPalListKind(V2),V1,V2)
p36: active#(U53(tt(),V1,V2)) -> isPalListKind#(V2)
p37: active#(U54(tt(),V1,V2)) -> U55#(isNeList(V1),V2)
p38: active#(U54(tt(),V1,V2)) -> isNeList#(V1)
p39: active#(U55(tt(),V2)) -> U56#(isList(V2))
p40: active#(U55(tt(),V2)) -> isList#(V2)
p41: active#(U61(tt(),V)) -> U62#(isPalListKind(V),V)
p42: active#(U61(tt(),V)) -> isPalListKind#(V)
p43: active#(U62(tt(),V)) -> U63#(isQid(V))
p44: active#(U62(tt(),V)) -> isQid#(V)
p45: active#(U71(tt(),I,P)) -> U72#(isPalListKind(I),P)
p46: active#(U71(tt(),I,P)) -> isPalListKind#(I)
p47: active#(U72(tt(),P)) -> U73#(isPal(P),P)
p48: active#(U72(tt(),P)) -> isPal#(P)
p49: active#(U73(tt(),P)) -> U74#(isPalListKind(P))
p50: active#(U73(tt(),P)) -> isPalListKind#(P)
p51: active#(U81(tt(),V)) -> U82#(isPalListKind(V),V)
p52: active#(U81(tt(),V)) -> isPalListKind#(V)
p53: active#(U82(tt(),V)) -> U83#(isNePal(V))
p54: active#(U82(tt(),V)) -> isNePal#(V)
p55: active#(U91(tt(),V2)) -> U92#(isPalListKind(V2))
p56: active#(U91(tt(),V2)) -> isPalListKind#(V2)
p57: active#(isList(V)) -> U11#(isPalListKind(V),V)
p58: active#(isList(V)) -> isPalListKind#(V)
p59: active#(isList(__(V1,V2))) -> U21#(isPalListKind(V1),V1,V2)
p60: active#(isList(__(V1,V2))) -> isPalListKind#(V1)
p61: active#(isNeList(V)) -> U31#(isPalListKind(V),V)
p62: active#(isNeList(V)) -> isPalListKind#(V)
p63: active#(isNeList(__(V1,V2))) -> U41#(isPalListKind(V1),V1,V2)
p64: active#(isNeList(__(V1,V2))) -> isPalListKind#(V1)
p65: active#(isNeList(__(V1,V2))) -> U51#(isPalListKind(V1),V1,V2)
p66: active#(isNeList(__(V1,V2))) -> isPalListKind#(V1)
p67: active#(isNePal(V)) -> U61#(isPalListKind(V),V)
p68: active#(isNePal(V)) -> isPalListKind#(V)
p69: active#(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),I,P)
p70: active#(isNePal(__(I,__(P,I)))) -> isQid#(I)
p71: active#(isPal(V)) -> U81#(isPalListKind(V),V)
p72: active#(isPal(V)) -> isPalListKind#(V)
p73: active#(isPalListKind(__(V1,V2))) -> U91#(isPalListKind(V1),V2)
p74: active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1)
p75: active#(__(X1,X2)) -> __#(active(X1),X2)
p76: active#(__(X1,X2)) -> active#(X1)
p77: active#(__(X1,X2)) -> __#(X1,active(X2))
p78: active#(__(X1,X2)) -> active#(X2)
p79: active#(U11(X1,X2)) -> U11#(active(X1),X2)
p80: active#(U11(X1,X2)) -> active#(X1)
p81: active#(U12(X1,X2)) -> U12#(active(X1),X2)
p82: active#(U12(X1,X2)) -> active#(X1)
p83: active#(U13(X)) -> U13#(active(X))
p84: active#(U13(X)) -> active#(X)
p85: active#(U21(X1,X2,X3)) -> U21#(active(X1),X2,X3)
p86: active#(U21(X1,X2,X3)) -> active#(X1)
p87: active#(U22(X1,X2,X3)) -> U22#(active(X1),X2,X3)
p88: active#(U22(X1,X2,X3)) -> active#(X1)
p89: active#(U23(X1,X2,X3)) -> U23#(active(X1),X2,X3)
p90: active#(U23(X1,X2,X3)) -> active#(X1)
p91: active#(U24(X1,X2,X3)) -> U24#(active(X1),X2,X3)
p92: active#(U24(X1,X2,X3)) -> active#(X1)
p93: active#(U25(X1,X2)) -> U25#(active(X1),X2)
p94: active#(U25(X1,X2)) -> active#(X1)
p95: active#(U26(X)) -> U26#(active(X))
p96: active#(U26(X)) -> active#(X)
p97: active#(U31(X1,X2)) -> U31#(active(X1),X2)
p98: active#(U31(X1,X2)) -> active#(X1)
p99: active#(U32(X1,X2)) -> U32#(active(X1),X2)
p100: active#(U32(X1,X2)) -> active#(X1)
p101: active#(U33(X)) -> U33#(active(X))
p102: active#(U33(X)) -> active#(X)
p103: active#(U41(X1,X2,X3)) -> U41#(active(X1),X2,X3)
p104: active#(U41(X1,X2,X3)) -> active#(X1)
p105: active#(U42(X1,X2,X3)) -> U42#(active(X1),X2,X3)
p106: active#(U42(X1,X2,X3)) -> active#(X1)
p107: active#(U43(X1,X2,X3)) -> U43#(active(X1),X2,X3)
p108: active#(U43(X1,X2,X3)) -> active#(X1)
p109: active#(U44(X1,X2,X3)) -> U44#(active(X1),X2,X3)
p110: active#(U44(X1,X2,X3)) -> active#(X1)
p111: active#(U45(X1,X2)) -> U45#(active(X1),X2)
p112: active#(U45(X1,X2)) -> active#(X1)
p113: active#(U46(X)) -> U46#(active(X))
p114: active#(U46(X)) -> active#(X)
p115: active#(U51(X1,X2,X3)) -> U51#(active(X1),X2,X3)
p116: active#(U51(X1,X2,X3)) -> active#(X1)
p117: active#(U52(X1,X2,X3)) -> U52#(active(X1),X2,X3)
p118: active#(U52(X1,X2,X3)) -> active#(X1)
p119: active#(U53(X1,X2,X3)) -> U53#(active(X1),X2,X3)
p120: active#(U53(X1,X2,X3)) -> active#(X1)
p121: active#(U54(X1,X2,X3)) -> U54#(active(X1),X2,X3)
p122: active#(U54(X1,X2,X3)) -> active#(X1)
p123: active#(U55(X1,X2)) -> U55#(active(X1),X2)
p124: active#(U55(X1,X2)) -> active#(X1)
p125: active#(U56(X)) -> U56#(active(X))
p126: active#(U56(X)) -> active#(X)
p127: active#(U61(X1,X2)) -> U61#(active(X1),X2)
p128: active#(U61(X1,X2)) -> active#(X1)
p129: active#(U62(X1,X2)) -> U62#(active(X1),X2)
p130: active#(U62(X1,X2)) -> active#(X1)
p131: active#(U63(X)) -> U63#(active(X))
p132: active#(U63(X)) -> active#(X)
p133: active#(U71(X1,X2,X3)) -> U71#(active(X1),X2,X3)
p134: active#(U71(X1,X2,X3)) -> active#(X1)
p135: active#(U72(X1,X2)) -> U72#(active(X1),X2)
p136: active#(U72(X1,X2)) -> active#(X1)
p137: active#(U73(X1,X2)) -> U73#(active(X1),X2)
p138: active#(U73(X1,X2)) -> active#(X1)
p139: active#(U74(X)) -> U74#(active(X))
p140: active#(U74(X)) -> active#(X)
p141: active#(U81(X1,X2)) -> U81#(active(X1),X2)
p142: active#(U81(X1,X2)) -> active#(X1)
p143: active#(U82(X1,X2)) -> U82#(active(X1),X2)
p144: active#(U82(X1,X2)) -> active#(X1)
p145: active#(U83(X)) -> U83#(active(X))
p146: active#(U83(X)) -> active#(X)
p147: active#(U91(X1,X2)) -> U91#(active(X1),X2)
p148: active#(U91(X1,X2)) -> active#(X1)
p149: active#(U92(X)) -> U92#(active(X))
p150: active#(U92(X)) -> active#(X)
p151: __#(mark(X1),X2) -> __#(X1,X2)
p152: __#(X1,mark(X2)) -> __#(X1,X2)
p153: U11#(mark(X1),X2) -> U11#(X1,X2)
p154: U12#(mark(X1),X2) -> U12#(X1,X2)
p155: U13#(mark(X)) -> U13#(X)
p156: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
p157: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3)
p158: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3)
p159: U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3)
p160: U25#(mark(X1),X2) -> U25#(X1,X2)
p161: U26#(mark(X)) -> U26#(X)
p162: U31#(mark(X1),X2) -> U31#(X1,X2)
p163: U32#(mark(X1),X2) -> U32#(X1,X2)
p164: U33#(mark(X)) -> U33#(X)
p165: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
p166: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
p167: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
p168: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
p169: U45#(mark(X1),X2) -> U45#(X1,X2)
p170: U46#(mark(X)) -> U46#(X)
p171: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
p172: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3)
p173: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3)
p174: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3)
p175: U55#(mark(X1),X2) -> U55#(X1,X2)
p176: U56#(mark(X)) -> U56#(X)
p177: U61#(mark(X1),X2) -> U61#(X1,X2)
p178: U62#(mark(X1),X2) -> U62#(X1,X2)
p179: U63#(mark(X)) -> U63#(X)
p180: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3)
p181: U72#(mark(X1),X2) -> U72#(X1,X2)
p182: U73#(mark(X1),X2) -> U73#(X1,X2)
p183: U74#(mark(X)) -> U74#(X)
p184: U81#(mark(X1),X2) -> U81#(X1,X2)
p185: U82#(mark(X1),X2) -> U82#(X1,X2)
p186: U83#(mark(X)) -> U83#(X)
p187: U91#(mark(X1),X2) -> U91#(X1,X2)
p188: U92#(mark(X)) -> U92#(X)
p189: proper#(__(X1,X2)) -> __#(proper(X1),proper(X2))
p190: proper#(__(X1,X2)) -> proper#(X1)
p191: proper#(__(X1,X2)) -> proper#(X2)
p192: proper#(U11(X1,X2)) -> U11#(proper(X1),proper(X2))
p193: proper#(U11(X1,X2)) -> proper#(X1)
p194: proper#(U11(X1,X2)) -> proper#(X2)
p195: proper#(U12(X1,X2)) -> U12#(proper(X1),proper(X2))
p196: proper#(U12(X1,X2)) -> proper#(X1)
p197: proper#(U12(X1,X2)) -> proper#(X2)
p198: proper#(isPalListKind(X)) -> isPalListKind#(proper(X))
p199: proper#(isPalListKind(X)) -> proper#(X)
p200: proper#(U13(X)) -> U13#(proper(X))
p201: proper#(U13(X)) -> proper#(X)
p202: proper#(isNeList(X)) -> isNeList#(proper(X))
p203: proper#(isNeList(X)) -> proper#(X)
p204: proper#(U21(X1,X2,X3)) -> U21#(proper(X1),proper(X2),proper(X3))
p205: proper#(U21(X1,X2,X3)) -> proper#(X1)
p206: proper#(U21(X1,X2,X3)) -> proper#(X2)
p207: proper#(U21(X1,X2,X3)) -> proper#(X3)
p208: proper#(U22(X1,X2,X3)) -> U22#(proper(X1),proper(X2),proper(X3))
p209: proper#(U22(X1,X2,X3)) -> proper#(X1)
p210: proper#(U22(X1,X2,X3)) -> proper#(X2)
p211: proper#(U22(X1,X2,X3)) -> proper#(X3)
p212: proper#(U23(X1,X2,X3)) -> U23#(proper(X1),proper(X2),proper(X3))
p213: proper#(U23(X1,X2,X3)) -> proper#(X1)
p214: proper#(U23(X1,X2,X3)) -> proper#(X2)
p215: proper#(U23(X1,X2,X3)) -> proper#(X3)
p216: proper#(U24(X1,X2,X3)) -> U24#(proper(X1),proper(X2),proper(X3))
p217: proper#(U24(X1,X2,X3)) -> proper#(X1)
p218: proper#(U24(X1,X2,X3)) -> proper#(X2)
p219: proper#(U24(X1,X2,X3)) -> proper#(X3)
p220: proper#(U25(X1,X2)) -> U25#(proper(X1),proper(X2))
p221: proper#(U25(X1,X2)) -> proper#(X1)
p222: proper#(U25(X1,X2)) -> proper#(X2)
p223: proper#(isList(X)) -> isList#(proper(X))
p224: proper#(isList(X)) -> proper#(X)
p225: proper#(U26(X)) -> U26#(proper(X))
p226: proper#(U26(X)) -> proper#(X)
p227: proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
p228: proper#(U31(X1,X2)) -> proper#(X1)
p229: proper#(U31(X1,X2)) -> proper#(X2)
p230: proper#(U32(X1,X2)) -> U32#(proper(X1),proper(X2))
p231: proper#(U32(X1,X2)) -> proper#(X1)
p232: proper#(U32(X1,X2)) -> proper#(X2)
p233: proper#(U33(X)) -> U33#(proper(X))
p234: proper#(U33(X)) -> proper#(X)
p235: proper#(isQid(X)) -> isQid#(proper(X))
p236: proper#(isQid(X)) -> proper#(X)
p237: proper#(U41(X1,X2,X3)) -> U41#(proper(X1),proper(X2),proper(X3))
p238: proper#(U41(X1,X2,X3)) -> proper#(X1)
p239: proper#(U41(X1,X2,X3)) -> proper#(X2)
p240: proper#(U41(X1,X2,X3)) -> proper#(X3)
p241: proper#(U42(X1,X2,X3)) -> U42#(proper(X1),proper(X2),proper(X3))
p242: proper#(U42(X1,X2,X3)) -> proper#(X1)
p243: proper#(U42(X1,X2,X3)) -> proper#(X2)
p244: proper#(U42(X1,X2,X3)) -> proper#(X3)
p245: proper#(U43(X1,X2,X3)) -> U43#(proper(X1),proper(X2),proper(X3))
p246: proper#(U43(X1,X2,X3)) -> proper#(X1)
p247: proper#(U43(X1,X2,X3)) -> proper#(X2)
p248: proper#(U43(X1,X2,X3)) -> proper#(X3)
p249: proper#(U44(X1,X2,X3)) -> U44#(proper(X1),proper(X2),proper(X3))
p250: proper#(U44(X1,X2,X3)) -> proper#(X1)
p251: proper#(U44(X1,X2,X3)) -> proper#(X2)
p252: proper#(U44(X1,X2,X3)) -> proper#(X3)
p253: proper#(U45(X1,X2)) -> U45#(proper(X1),proper(X2))
p254: proper#(U45(X1,X2)) -> proper#(X1)
p255: proper#(U45(X1,X2)) -> proper#(X2)
p256: proper#(U46(X)) -> U46#(proper(X))
p257: proper#(U46(X)) -> proper#(X)
p258: proper#(U51(X1,X2,X3)) -> U51#(proper(X1),proper(X2),proper(X3))
p259: proper#(U51(X1,X2,X3)) -> proper#(X1)
p260: proper#(U51(X1,X2,X3)) -> proper#(X2)
p261: proper#(U51(X1,X2,X3)) -> proper#(X3)
p262: proper#(U52(X1,X2,X3)) -> U52#(proper(X1),proper(X2),proper(X3))
p263: proper#(U52(X1,X2,X3)) -> proper#(X1)
p264: proper#(U52(X1,X2,X3)) -> proper#(X2)
p265: proper#(U52(X1,X2,X3)) -> proper#(X3)
p266: proper#(U53(X1,X2,X3)) -> U53#(proper(X1),proper(X2),proper(X3))
p267: proper#(U53(X1,X2,X3)) -> proper#(X1)
p268: proper#(U53(X1,X2,X3)) -> proper#(X2)
p269: proper#(U53(X1,X2,X3)) -> proper#(X3)
p270: proper#(U54(X1,X2,X3)) -> U54#(proper(X1),proper(X2),proper(X3))
p271: proper#(U54(X1,X2,X3)) -> proper#(X1)
p272: proper#(U54(X1,X2,X3)) -> proper#(X2)
p273: proper#(U54(X1,X2,X3)) -> proper#(X3)
p274: proper#(U55(X1,X2)) -> U55#(proper(X1),proper(X2))
p275: proper#(U55(X1,X2)) -> proper#(X1)
p276: proper#(U55(X1,X2)) -> proper#(X2)
p277: proper#(U56(X)) -> U56#(proper(X))
p278: proper#(U56(X)) -> proper#(X)
p279: proper#(U61(X1,X2)) -> U61#(proper(X1),proper(X2))
p280: proper#(U61(X1,X2)) -> proper#(X1)
p281: proper#(U61(X1,X2)) -> proper#(X2)
p282: proper#(U62(X1,X2)) -> U62#(proper(X1),proper(X2))
p283: proper#(U62(X1,X2)) -> proper#(X1)
p284: proper#(U62(X1,X2)) -> proper#(X2)
p285: proper#(U63(X)) -> U63#(proper(X))
p286: proper#(U63(X)) -> proper#(X)
p287: proper#(U71(X1,X2,X3)) -> U71#(proper(X1),proper(X2),proper(X3))
p288: proper#(U71(X1,X2,X3)) -> proper#(X1)
p289: proper#(U71(X1,X2,X3)) -> proper#(X2)
p290: proper#(U71(X1,X2,X3)) -> proper#(X3)
p291: proper#(U72(X1,X2)) -> U72#(proper(X1),proper(X2))
p292: proper#(U72(X1,X2)) -> proper#(X1)
p293: proper#(U72(X1,X2)) -> proper#(X2)
p294: proper#(U73(X1,X2)) -> U73#(proper(X1),proper(X2))
p295: proper#(U73(X1,X2)) -> proper#(X1)
p296: proper#(U73(X1,X2)) -> proper#(X2)
p297: proper#(isPal(X)) -> isPal#(proper(X))
p298: proper#(isPal(X)) -> proper#(X)
p299: proper#(U74(X)) -> U74#(proper(X))
p300: proper#(U74(X)) -> proper#(X)
p301: proper#(U81(X1,X2)) -> U81#(proper(X1),proper(X2))
p302: proper#(U81(X1,X2)) -> proper#(X1)
p303: proper#(U81(X1,X2)) -> proper#(X2)
p304: proper#(U82(X1,X2)) -> U82#(proper(X1),proper(X2))
p305: proper#(U82(X1,X2)) -> proper#(X1)
p306: proper#(U82(X1,X2)) -> proper#(X2)
p307: proper#(U83(X)) -> U83#(proper(X))
p308: proper#(U83(X)) -> proper#(X)
p309: proper#(isNePal(X)) -> isNePal#(proper(X))
p310: proper#(isNePal(X)) -> proper#(X)
p311: proper#(U91(X1,X2)) -> U91#(proper(X1),proper(X2))
p312: proper#(U91(X1,X2)) -> proper#(X1)
p313: proper#(U91(X1,X2)) -> proper#(X2)
p314: proper#(U92(X)) -> U92#(proper(X))
p315: proper#(U92(X)) -> proper#(X)
p316: __#(ok(X1),ok(X2)) -> __#(X1,X2)
p317: U11#(ok(X1),ok(X2)) -> U11#(X1,X2)
p318: U12#(ok(X1),ok(X2)) -> U12#(X1,X2)
p319: isPalListKind#(ok(X)) -> isPalListKind#(X)
p320: U13#(ok(X)) -> U13#(X)
p321: isNeList#(ok(X)) -> isNeList#(X)
p322: U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3)
p323: U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3)
p324: U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3)
p325: U24#(ok(X1),ok(X2),ok(X3)) -> U24#(X1,X2,X3)
p326: U25#(ok(X1),ok(X2)) -> U25#(X1,X2)
p327: isList#(ok(X)) -> isList#(X)
p328: U26#(ok(X)) -> U26#(X)
p329: U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
p330: U32#(ok(X1),ok(X2)) -> U32#(X1,X2)
p331: U33#(ok(X)) -> U33#(X)
p332: isQid#(ok(X)) -> isQid#(X)
p333: U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)
p334: U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)
p335: U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)
p336: U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)
p337: U45#(ok(X1),ok(X2)) -> U45#(X1,X2)
p338: U46#(ok(X)) -> U46#(X)
p339: U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3)
p340: U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3)
p341: U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3)
p342: U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3)
p343: U55#(ok(X1),ok(X2)) -> U55#(X1,X2)
p344: U56#(ok(X)) -> U56#(X)
p345: U61#(ok(X1),ok(X2)) -> U61#(X1,X2)
p346: U62#(ok(X1),ok(X2)) -> U62#(X1,X2)
p347: U63#(ok(X)) -> U63#(X)
p348: U71#(ok(X1),ok(X2),ok(X3)) -> U71#(X1,X2,X3)
p349: U72#(ok(X1),ok(X2)) -> U72#(X1,X2)
p350: U73#(ok(X1),ok(X2)) -> U73#(X1,X2)
p351: isPal#(ok(X)) -> isPal#(X)
p352: U74#(ok(X)) -> U74#(X)
p353: U81#(ok(X1),ok(X2)) -> U81#(X1,X2)
p354: U82#(ok(X1),ok(X2)) -> U82#(X1,X2)
p355: U83#(ok(X)) -> U83#(X)
p356: isNePal#(ok(X)) -> isNePal#(X)
p357: U91#(ok(X1),ok(X2)) -> U91#(X1,X2)
p358: U92#(ok(X)) -> U92#(X)
p359: top#(mark(X)) -> top#(proper(X))
p360: top#(mark(X)) -> proper#(X)
p361: top#(ok(X)) -> top#(active(X))
p362: top#(ok(X)) -> active#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p359, p361}
  {p76, p78, p80, p82, p84, p86, p88, p90, p92, p94, p96, p98, p100, p102, p104, p106, p108, p110, p112, p114, p116, p118, p120, p122, p124, p126, p128, p130, p132, p134, p136, p138, p140, p142, p144, p146, p148, p150}
  {p190, p191, p193, p194, p196, p197, p199, p201, p203, p205, p206, p207, p209, p210, p211, p213, p214, p215, p217, p218, p219, p221, p222, p224, p226, p228, p229, p231, p232, p234, p236, p238, p239, p240, p242, p243, p244, p246, p247, p248, p250, p251, p252, p254, p255, p257, p259, p260, p261, p263, p264, p265, p267, p268, p269, p271, p272, p273, p275, p276, p278, p280, p281, p283, p284, p286, p288, p289, p290, p292, p293, p295, p296, p298, p300, p302, p303, p305, p306, p308, p310, p312, p313, p315}
  {p151, p152, p316}
  {p154, p318}
  {p319}
  {p155, p320}
  {p321}
  {p157, p323}
  {p158, p324}
  {p159, p325}
  {p160, p326}
  {p327}
  {p161, p328}
  {p163, p330}
  {p164, p331}
  {p332}
  {p166, p334}
  {p167, p335}
  {p168, p336}
  {p169, p337}
  {p170, p338}
  {p172, p340}
  {p173, p341}
  {p174, p342}
  {p175, p343}
  {p176, p344}
  {p178, p346}
  {p179, p347}
  {p181, p349}
  {p182, p350}
  {p351}
  {p183, p352}
  {p185, p354}
  {p186, p355}
  {p356}
  {p188, p358}
  {p153, p317}
  {p156, p322}
  {p162, p329}
  {p165, p333}
  {p171, p339}
  {p177, p345}
  {p180, p348}
  {p184, p353}
  {p187, p357}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: top#(ok(X)) -> top#(active(X))
p2: top#(mark(X)) -> top#(proper(X))

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      nil > active > u > o > i > e > a > __ > U71 > U72 > isPal > U81 > U82 > isNePal > U61 > U21 > U51 > U41 > U91 > U83 > U73 > U74 > U62 > U63 > U52 > U53 > U54 > U55 > U56 > U42 > U43 > U44 > U22 > U23 > U24 > U25 > isList > U45 > U11 > U12 > isNeList > U31 > isPalListKind > U92 > U32 > isQid > tt > U46 > U33 > U26 > U13 > top# > ok > proper > mark
    
    argument filter:
  
      pi(top#) = 1
      pi(ok) = 1
      pi(active) = 1
      pi(mark) = [1]
      pi(proper) = 1
      pi(__) = [1, 2]
      pi(U11) = [1, 2]
      pi(U12) = [1, 2]
      pi(U13) = [1]
      pi(U21) = [1, 2, 3]
      pi(U22) = [1, 2, 3]
      pi(U23) = [1, 2, 3]
      pi(U24) = [1, 2, 3]
      pi(U25) = [1, 2]
      pi(U26) = [1]
      pi(U31) = [1, 2]
      pi(U32) = [1, 2]
      pi(U33) = [1]
      pi(U41) = [1, 2, 3]
      pi(U42) = [1, 2, 3]
      pi(U43) = [1, 2, 3]
      pi(U44) = [1, 2, 3]
      pi(U45) = [1, 2]
      pi(U46) = [1]
      pi(U51) = [1, 2, 3]
      pi(U52) = [1, 2, 3]
      pi(U53) = [1, 2, 3]
      pi(U54) = [1, 2, 3]
      pi(U55) = [1, 2]
      pi(U56) = [1]
      pi(U61) = [1, 2]
      pi(U62) = [1, 2]
      pi(U63) = [1]
      pi(U71) = [1, 2, 3]
      pi(U72) = [1, 2]
      pi(U73) = [1, 2]
      pi(U74) = [1]
      pi(U81) = [1, 2]
      pi(U82) = [1, 2]
      pi(U83) = [1]
      pi(U91) = [1, 2]
      pi(U92) = [1]
      pi(isPalListKind) = [1]
      pi(isNeList) = [1]
      pi(isList) = [1]
      pi(isQid) = [1]
      pi(isPal) = [1]
      pi(isNePal) = [1]
      pi(nil) = []
      pi(tt) = []
      pi(a) = []
      pi(e) = []
      pi(i) = []
      pi(o) = []
      pi(u) = []

The next rules are strictly ordered:

  p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r231, r232

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: top#(ok(X)) -> top#(active(X))

and R consists of:

r1: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r2: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r3: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r4: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r5: U13(ok(X)) -> ok(U13(X))
r6: isNeList(ok(X)) -> ok(isNeList(X))
r7: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r8: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r9: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r10: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r11: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r12: isList(ok(X)) -> ok(isList(X))
r13: U26(ok(X)) -> ok(U26(X))
r14: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r15: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r16: U33(ok(X)) -> ok(U33(X))
r17: isQid(ok(X)) -> ok(isQid(X))
r18: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r19: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r20: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r21: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r22: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r23: U46(ok(X)) -> ok(U46(X))
r24: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r25: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r26: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r27: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r28: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r29: U56(ok(X)) -> ok(U56(X))
r30: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r31: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r32: U63(ok(X)) -> ok(U63(X))
r33: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r34: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r35: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r36: isPal(ok(X)) -> ok(isPal(X))
r37: U74(ok(X)) -> ok(U74(X))
r38: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r39: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r40: U83(ok(X)) -> ok(U83(X))
r41: isNePal(ok(X)) -> ok(isNePal(X))
r42: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r43: U92(ok(X)) -> ok(U92(X))
r44: active(__(X1,X2)) -> __(active(X1),X2)
r45: active(__(X1,X2)) -> __(X1,active(X2))
r46: active(U11(X1,X2)) -> U11(active(X1),X2)
r47: active(U12(X1,X2)) -> U12(active(X1),X2)
r48: active(U13(X)) -> U13(active(X))
r49: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r50: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r51: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r52: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r53: active(U25(X1,X2)) -> U25(active(X1),X2)
r54: active(U26(X)) -> U26(active(X))
r55: active(U31(X1,X2)) -> U31(active(X1),X2)
r56: active(U32(X1,X2)) -> U32(active(X1),X2)
r57: active(U33(X)) -> U33(active(X))
r58: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r59: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r60: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r61: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r62: active(U45(X1,X2)) -> U45(active(X1),X2)
r63: active(U46(X)) -> U46(active(X))
r64: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r65: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r66: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r67: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r68: active(U55(X1,X2)) -> U55(active(X1),X2)
r69: active(U56(X)) -> U56(active(X))
r70: active(U61(X1,X2)) -> U61(active(X1),X2)
r71: active(U62(X1,X2)) -> U62(active(X1),X2)
r72: active(U63(X)) -> U63(active(X))
r73: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r74: active(U72(X1,X2)) -> U72(active(X1),X2)
r75: active(U73(X1,X2)) -> U73(active(X1),X2)
r76: active(U74(X)) -> U74(active(X))
r77: active(U81(X1,X2)) -> U81(active(X1),X2)
r78: active(U82(X1,X2)) -> U82(active(X1),X2)
r79: active(U83(X)) -> U83(active(X))
r80: active(U91(X1,X2)) -> U91(active(X1),X2)
r81: active(U92(X)) -> U92(active(X))
r82: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r83: proper(nil()) -> ok(nil())
r84: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r85: proper(tt()) -> ok(tt())
r86: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r87: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r88: proper(U13(X)) -> U13(proper(X))
r89: proper(isNeList(X)) -> isNeList(proper(X))
r90: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r91: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r92: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r93: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r94: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r95: proper(isList(X)) -> isList(proper(X))
r96: proper(U26(X)) -> U26(proper(X))
r97: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r98: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r99: proper(U33(X)) -> U33(proper(X))
r100: proper(isQid(X)) -> isQid(proper(X))
r101: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r102: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r103: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r104: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r105: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r106: proper(U46(X)) -> U46(proper(X))
r107: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r108: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r109: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r110: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r111: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r112: proper(U56(X)) -> U56(proper(X))
r113: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r114: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r115: proper(U63(X)) -> U63(proper(X))
r116: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r117: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r118: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r119: proper(isPal(X)) -> isPal(proper(X))
r120: proper(U74(X)) -> U74(proper(X))
r121: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r122: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r123: proper(U83(X)) -> U83(proper(X))
r124: proper(isNePal(X)) -> isNePal(proper(X))
r125: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r126: proper(U92(X)) -> U92(proper(X))
r127: proper(a()) -> ok(a())
r128: proper(e()) -> ok(e())
r129: proper(i()) -> ok(i())
r130: proper(o()) -> ok(o())
r131: proper(u()) -> ok(u())

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: top#(ok(X)) -> top#(active(X))

and R consists of:

r1: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r2: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r3: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r4: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r5: U13(ok(X)) -> ok(U13(X))
r6: isNeList(ok(X)) -> ok(isNeList(X))
r7: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r8: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r9: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r10: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r11: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r12: isList(ok(X)) -> ok(isList(X))
r13: U26(ok(X)) -> ok(U26(X))
r14: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r15: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r16: U33(ok(X)) -> ok(U33(X))
r17: isQid(ok(X)) -> ok(isQid(X))
r18: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r19: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r20: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r21: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r22: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r23: U46(ok(X)) -> ok(U46(X))
r24: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r25: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r26: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r27: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r28: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r29: U56(ok(X)) -> ok(U56(X))
r30: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r31: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r32: U63(ok(X)) -> ok(U63(X))
r33: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r34: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r35: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r36: isPal(ok(X)) -> ok(isPal(X))
r37: U74(ok(X)) -> ok(U74(X))
r38: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r39: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r40: U83(ok(X)) -> ok(U83(X))
r41: isNePal(ok(X)) -> ok(isNePal(X))
r42: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r43: U92(ok(X)) -> ok(U92(X))
r44: active(__(X1,X2)) -> __(active(X1),X2)
r45: active(__(X1,X2)) -> __(X1,active(X2))
r46: active(U11(X1,X2)) -> U11(active(X1),X2)
r47: active(U12(X1,X2)) -> U12(active(X1),X2)
r48: active(U13(X)) -> U13(active(X))
r49: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r50: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r51: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r52: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r53: active(U25(X1,X2)) -> U25(active(X1),X2)
r54: active(U26(X)) -> U26(active(X))
r55: active(U31(X1,X2)) -> U31(active(X1),X2)
r56: active(U32(X1,X2)) -> U32(active(X1),X2)
r57: active(U33(X)) -> U33(active(X))
r58: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r59: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r60: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r61: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r62: active(U45(X1,X2)) -> U45(active(X1),X2)
r63: active(U46(X)) -> U46(active(X))
r64: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r65: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r66: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r67: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r68: active(U55(X1,X2)) -> U55(active(X1),X2)
r69: active(U56(X)) -> U56(active(X))
r70: active(U61(X1,X2)) -> U61(active(X1),X2)
r71: active(U62(X1,X2)) -> U62(active(X1),X2)
r72: active(U63(X)) -> U63(active(X))
r73: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r74: active(U72(X1,X2)) -> U72(active(X1),X2)
r75: active(U73(X1,X2)) -> U73(active(X1),X2)
r76: active(U74(X)) -> U74(active(X))
r77: active(U81(X1,X2)) -> U81(active(X1),X2)
r78: active(U82(X1,X2)) -> U82(active(X1),X2)
r79: active(U83(X)) -> U83(active(X))
r80: active(U91(X1,X2)) -> U91(active(X1),X2)
r81: active(U92(X)) -> U92(active(X))
r82: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r83: proper(nil()) -> ok(nil())
r84: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r85: proper(tt()) -> ok(tt())
r86: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r87: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r88: proper(U13(X)) -> U13(proper(X))
r89: proper(isNeList(X)) -> isNeList(proper(X))
r90: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r91: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r92: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r93: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r94: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r95: proper(isList(X)) -> isList(proper(X))
r96: proper(U26(X)) -> U26(proper(X))
r97: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r98: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r99: proper(U33(X)) -> U33(proper(X))
r100: proper(isQid(X)) -> isQid(proper(X))
r101: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r102: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r103: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r104: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r105: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r106: proper(U46(X)) -> U46(proper(X))
r107: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r108: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r109: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r110: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r111: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r112: proper(U56(X)) -> U56(proper(X))
r113: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r114: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r115: proper(U63(X)) -> U63(proper(X))
r116: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r117: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r118: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r119: proper(isPal(X)) -> isPal(proper(X))
r120: proper(U74(X)) -> U74(proper(X))
r121: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r122: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r123: proper(U83(X)) -> U83(proper(X))
r124: proper(isNePal(X)) -> isNePal(proper(X))
r125: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r126: proper(U92(X)) -> U92(proper(X))
r127: proper(a()) -> ok(a())
r128: proper(e()) -> ok(e())
r129: proper(i()) -> ok(i())
r130: proper(o()) -> ok(o())
r131: proper(u()) -> ok(u())

The set of usable rules consists of

  r1, r2, r3, r5, r7, r8, r9, r10, r11, r13, r14, r15, r16, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r37, r38, r39, r40, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U73 > U72 > U71 > U63 > U61 > U56 > U52 > U46 > U26 > U23 > U45 > U44 > U33 > U12 > ok > active > U92 > U74 > U51 > U91 > U83 > __ > U82 > U81 > U62 > U55 > U54 > U53 > U43 > U42 > U41 > U32 > U31 > U25 > U24 > U22 > U21 > U13 > U11 > top#
    
    argument filter:
  
      pi(top#) = [1]
      pi(ok) = [1]
      pi(active) = [1]
      pi(__) = 1
      pi(U11) = 1
      pi(U12) = 2
      pi(U13) = 1
      pi(U21) = 3
      pi(U22) = 3
      pi(U23) = [3]
      pi(U24) = 2
      pi(U25) = 1
      pi(U26) = 1
      pi(U31) = 2
      pi(U32) = 1
      pi(U33) = 1
      pi(U41) = 1
      pi(U42) = 3
      pi(U43) = 3
      pi(U44) = 2
      pi(U45) = 2
      pi(U46) = 1
      pi(U51) = 3
      pi(U52) = 2
      pi(U53) = 2
      pi(U54) = 1
      pi(U55) = 1
      pi(U56) = 1
      pi(U61) = 2
      pi(U62) = 1
      pi(U63) = 1
      pi(U71) = 1
      pi(U72) = 1
      pi(U73) = 2
      pi(U74) = 1
      pi(U81) = 2
      pi(U82) = 2
      pi(U83) = 1
      pi(U91) = 2
      pi(U92) = 1

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: active#(U92(X)) -> active#(X)
p2: active#(U91(X1,X2)) -> active#(X1)
p3: active#(U83(X)) -> active#(X)
p4: active#(U82(X1,X2)) -> active#(X1)
p5: active#(U81(X1,X2)) -> active#(X1)
p6: active#(U74(X)) -> active#(X)
p7: active#(U73(X1,X2)) -> active#(X1)
p8: active#(U72(X1,X2)) -> active#(X1)
p9: active#(U71(X1,X2,X3)) -> active#(X1)
p10: active#(U63(X)) -> active#(X)
p11: active#(U62(X1,X2)) -> active#(X1)
p12: active#(U61(X1,X2)) -> active#(X1)
p13: active#(U56(X)) -> active#(X)
p14: active#(U55(X1,X2)) -> active#(X1)
p15: active#(U54(X1,X2,X3)) -> active#(X1)
p16: active#(U53(X1,X2,X3)) -> active#(X1)
p17: active#(U52(X1,X2,X3)) -> active#(X1)
p18: active#(U51(X1,X2,X3)) -> active#(X1)
p19: active#(U46(X)) -> active#(X)
p20: active#(U45(X1,X2)) -> active#(X1)
p21: active#(U44(X1,X2,X3)) -> active#(X1)
p22: active#(U43(X1,X2,X3)) -> active#(X1)
p23: active#(U42(X1,X2,X3)) -> active#(X1)
p24: active#(U41(X1,X2,X3)) -> active#(X1)
p25: active#(U33(X)) -> active#(X)
p26: active#(U32(X1,X2)) -> active#(X1)
p27: active#(U31(X1,X2)) -> active#(X1)
p28: active#(U26(X)) -> active#(X)
p29: active#(U25(X1,X2)) -> active#(X1)
p30: active#(U24(X1,X2,X3)) -> active#(X1)
p31: active#(U23(X1,X2,X3)) -> active#(X1)
p32: active#(U22(X1,X2,X3)) -> active#(X1)
p33: active#(U21(X1,X2,X3)) -> active#(X1)
p34: active#(U13(X)) -> active#(X)
p35: active#(U12(X1,X2)) -> active#(X1)
p36: active#(U11(X1,X2)) -> active#(X1)
p37: active#(__(X1,X2)) -> active#(X2)
p38: active#(__(X1,X2)) -> active#(X1)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      active# > __ > U11 > U12 > U13 > U62 > U21 > U22 > U23 > U24 > U25 > U26 > U31 > U32 > U33 > U41 > U42 > U43 > U44 > U45 > U46 > U51 > U52 > U53 > U54 > U71 > U55 > U56 > U61 > U63 > U72 > U73 > U74 > U81 > U82 > U83 > U91 > U92
    
    argument filter:
  
      pi(active#) = 1
      pi(U92) = [1]
      pi(U91) = [1, 2]
      pi(U83) = [1]
      pi(U82) = [1, 2]
      pi(U81) = [1, 2]
      pi(U74) = [1]
      pi(U73) = [1, 2]
      pi(U72) = [1, 2]
      pi(U71) = [1, 2, 3]
      pi(U63) = [1]
      pi(U62) = [1, 2]
      pi(U61) = [1, 2]
      pi(U56) = [1]
      pi(U55) = [1, 2]
      pi(U54) = [1, 2, 3]
      pi(U53) = [1, 2, 3]
      pi(U52) = [1, 2, 3]
      pi(U51) = [1, 2, 3]
      pi(U46) = [1]
      pi(U45) = [1, 2]
      pi(U44) = [1, 2, 3]
      pi(U43) = [1, 2, 3]
      pi(U42) = [1, 2, 3]
      pi(U41) = [1, 2, 3]
      pi(U33) = [1]
      pi(U32) = [1, 2]
      pi(U31) = [1, 2]
      pi(U26) = [1]
      pi(U25) = [1, 2]
      pi(U24) = [1, 2, 3]
      pi(U23) = [1, 2, 3]
      pi(U22) = [1, 2, 3]
      pi(U21) = [1, 2, 3]
      pi(U13) = [1]
      pi(U12) = [1, 2]
      pi(U11) = [1, 2]
      pi(__) = [1, 2]

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36, p37, p38
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: proper#(U92(X)) -> proper#(X)
p2: proper#(U91(X1,X2)) -> proper#(X2)
p3: proper#(U91(X1,X2)) -> proper#(X1)
p4: proper#(isNePal(X)) -> proper#(X)
p5: proper#(U83(X)) -> proper#(X)
p6: proper#(U82(X1,X2)) -> proper#(X2)
p7: proper#(U82(X1,X2)) -> proper#(X1)
p8: proper#(U81(X1,X2)) -> proper#(X2)
p9: proper#(U81(X1,X2)) -> proper#(X1)
p10: proper#(U74(X)) -> proper#(X)
p11: proper#(isPal(X)) -> proper#(X)
p12: proper#(U73(X1,X2)) -> proper#(X2)
p13: proper#(U73(X1,X2)) -> proper#(X1)
p14: proper#(U72(X1,X2)) -> proper#(X2)
p15: proper#(U72(X1,X2)) -> proper#(X1)
p16: proper#(U71(X1,X2,X3)) -> proper#(X3)
p17: proper#(U71(X1,X2,X3)) -> proper#(X2)
p18: proper#(U71(X1,X2,X3)) -> proper#(X1)
p19: proper#(U63(X)) -> proper#(X)
p20: proper#(U62(X1,X2)) -> proper#(X2)
p21: proper#(U62(X1,X2)) -> proper#(X1)
p22: proper#(U61(X1,X2)) -> proper#(X2)
p23: proper#(U61(X1,X2)) -> proper#(X1)
p24: proper#(U56(X)) -> proper#(X)
p25: proper#(U55(X1,X2)) -> proper#(X2)
p26: proper#(U55(X1,X2)) -> proper#(X1)
p27: proper#(U54(X1,X2,X3)) -> proper#(X3)
p28: proper#(U54(X1,X2,X3)) -> proper#(X2)
p29: proper#(U54(X1,X2,X3)) -> proper#(X1)
p30: proper#(U53(X1,X2,X3)) -> proper#(X3)
p31: proper#(U53(X1,X2,X3)) -> proper#(X2)
p32: proper#(U53(X1,X2,X3)) -> proper#(X1)
p33: proper#(U52(X1,X2,X3)) -> proper#(X3)
p34: proper#(U52(X1,X2,X3)) -> proper#(X2)
p35: proper#(U52(X1,X2,X3)) -> proper#(X1)
p36: proper#(U51(X1,X2,X3)) -> proper#(X3)
p37: proper#(U51(X1,X2,X3)) -> proper#(X2)
p38: proper#(U51(X1,X2,X3)) -> proper#(X1)
p39: proper#(U46(X)) -> proper#(X)
p40: proper#(U45(X1,X2)) -> proper#(X2)
p41: proper#(U45(X1,X2)) -> proper#(X1)
p42: proper#(U44(X1,X2,X3)) -> proper#(X3)
p43: proper#(U44(X1,X2,X3)) -> proper#(X2)
p44: proper#(U44(X1,X2,X3)) -> proper#(X1)
p45: proper#(U43(X1,X2,X3)) -> proper#(X3)
p46: proper#(U43(X1,X2,X3)) -> proper#(X2)
p47: proper#(U43(X1,X2,X3)) -> proper#(X1)
p48: proper#(U42(X1,X2,X3)) -> proper#(X3)
p49: proper#(U42(X1,X2,X3)) -> proper#(X2)
p50: proper#(U42(X1,X2,X3)) -> proper#(X1)
p51: proper#(U41(X1,X2,X3)) -> proper#(X3)
p52: proper#(U41(X1,X2,X3)) -> proper#(X2)
p53: proper#(U41(X1,X2,X3)) -> proper#(X1)
p54: proper#(isQid(X)) -> proper#(X)
p55: proper#(U33(X)) -> proper#(X)
p56: proper#(U32(X1,X2)) -> proper#(X2)
p57: proper#(U32(X1,X2)) -> proper#(X1)
p58: proper#(U31(X1,X2)) -> proper#(X2)
p59: proper#(U31(X1,X2)) -> proper#(X1)
p60: proper#(U26(X)) -> proper#(X)
p61: proper#(isList(X)) -> proper#(X)
p62: proper#(U25(X1,X2)) -> proper#(X2)
p63: proper#(U25(X1,X2)) -> proper#(X1)
p64: proper#(U24(X1,X2,X3)) -> proper#(X3)
p65: proper#(U24(X1,X2,X3)) -> proper#(X2)
p66: proper#(U24(X1,X2,X3)) -> proper#(X1)
p67: proper#(U23(X1,X2,X3)) -> proper#(X3)
p68: proper#(U23(X1,X2,X3)) -> proper#(X2)
p69: proper#(U23(X1,X2,X3)) -> proper#(X1)
p70: proper#(U22(X1,X2,X3)) -> proper#(X3)
p71: proper#(U22(X1,X2,X3)) -> proper#(X2)
p72: proper#(U22(X1,X2,X3)) -> proper#(X1)
p73: proper#(U21(X1,X2,X3)) -> proper#(X3)
p74: proper#(U21(X1,X2,X3)) -> proper#(X2)
p75: proper#(U21(X1,X2,X3)) -> proper#(X1)
p76: proper#(isNeList(X)) -> proper#(X)
p77: proper#(U13(X)) -> proper#(X)
p78: proper#(isPalListKind(X)) -> proper#(X)
p79: proper#(U12(X1,X2)) -> proper#(X2)
p80: proper#(U12(X1,X2)) -> proper#(X1)
p81: proper#(U11(X1,X2)) -> proper#(X2)
p82: proper#(U11(X1,X2)) -> proper#(X1)
p83: proper#(__(X1,X2)) -> proper#(X2)
p84: proper#(__(X1,X2)) -> proper#(X1)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      proper# > __ > U11 > U12 > isPalListKind > U13 > isNeList > U21 > U22 > U23 > U24 > U25 > isList > U26 > U51 > U31 > U32 > U33 > isQid > U41 > U42 > U43 > U44 > U45 > U46 > U52 > U53 > U54 > U55 > U56 > U61 > U62 > U63 > U71 > U72 > U73 > isPal > U74 > U81 > U82 > U83 > isNePal > U91 > U92
    
    argument filter:
  
      pi(proper#) = 1
      pi(U92) = [1]
      pi(U91) = [1, 2]
      pi(isNePal) = [1]
      pi(U83) = [1]
      pi(U82) = [1, 2]
      pi(U81) = [1, 2]
      pi(U74) = [1]
      pi(isPal) = [1]
      pi(U73) = [1, 2]
      pi(U72) = [1, 2]
      pi(U71) = [1, 2, 3]
      pi(U63) = [1]
      pi(U62) = [1, 2]
      pi(U61) = [1, 2]
      pi(U56) = [1]
      pi(U55) = [1, 2]
      pi(U54) = [1, 2, 3]
      pi(U53) = [1, 2, 3]
      pi(U52) = [1, 2, 3]
      pi(U51) = [1, 2, 3]
      pi(U46) = [1]
      pi(U45) = [1, 2]
      pi(U44) = [1, 2, 3]
      pi(U43) = [1, 2, 3]
      pi(U42) = [1, 2, 3]
      pi(U41) = [1, 2, 3]
      pi(isQid) = [1]
      pi(U33) = [1]
      pi(U32) = [1, 2]
      pi(U31) = [1, 2]
      pi(U26) = [1]
      pi(isList) = [1]
      pi(U25) = [1, 2]
      pi(U24) = [1, 2, 3]
      pi(U23) = [1, 2, 3]
      pi(U22) = [1, 2, 3]
      pi(U21) = [1, 2, 3]
      pi(isNeList) = [1]
      pi(U13) = [1]
      pi(isPalListKind) = [1]
      pi(U12) = [1, 2]
      pi(U11) = [1, 2]
      pi(__) = [1, 2]

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36, p37, p38, p39, p40, p41, p42, p43, p44, p45, p46, p47, p48, p49, p50, p51, p52, p53, p54, p55, p56, p57, p58, p59, p60, p61, p62, p63, p64, p65, p66, p67, p68, p69, p70, p71, p72, p73, p74, p75, p76, p77, p78, p79, p80, p81, p82, p83, p84
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: __#(mark(X1),X2) -> __#(X1,X2)
p2: __#(ok(X1),ok(X2)) -> __#(X1,X2)
p3: __#(X1,mark(X2)) -> __#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      __# > ok > mark
    
    argument filter:
  
      pi(__#) = 2
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p2, p3

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: __#(mark(X1),X2) -> __#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: __#(mark(X1),X2) -> __#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > __#
    
    argument filter:
  
      pi(__#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U12#(mark(X1),X2) -> U12#(X1,X2)
p2: U12#(ok(X1),ok(X2)) -> U12#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U12# > ok > mark
    
    argument filter:
  
      pi(U12#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U12#(mark(X1),X2) -> U12#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U12#(mark(X1),X2) -> U12#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U12#
    
    argument filter:
  
      pi(U12#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: isPalListKind#(ok(X)) -> isPalListKind#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      ok > isPalListKind#
    
    argument filter:
  
      pi(isPalListKind#) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U13#(mark(X)) -> U13#(X)
p2: U13#(ok(X)) -> U13#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U13# > ok > mark
    
    argument filter:
  
      pi(U13#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: isNeList#(ok(X)) -> isNeList#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      ok > isNeList#
    
    argument filter:
  
      pi(isNeList#) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3)
p2: U22#(ok(X1),ok(X2),ok(X3)) -> U22#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U22# > ok > mark
    
    argument filter:
  
      pi(U22#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U22# > mark
    
    argument filter:
  
      pi(U22#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3)
p2: U23#(ok(X1),ok(X2),ok(X3)) -> U23#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U23# > ok > mark
    
    argument filter:
  
      pi(U23#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U23# > mark
    
    argument filter:
  
      pi(U23#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3)
p2: U24#(ok(X1),ok(X2),ok(X3)) -> U24#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U24# > ok > mark
    
    argument filter:
  
      pi(U24#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U24# > mark
    
    argument filter:
  
      pi(U24#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U25#(mark(X1),X2) -> U25#(X1,X2)
p2: U25#(ok(X1),ok(X2)) -> U25#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U25# > ok > mark
    
    argument filter:
  
      pi(U25#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U25#(mark(X1),X2) -> U25#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U25#(mark(X1),X2) -> U25#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U25#
    
    argument filter:
  
      pi(U25#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: isList#(ok(X)) -> isList#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      ok > isList#
    
    argument filter:
  
      pi(isList#) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U26#(mark(X)) -> U26#(X)
p2: U26#(ok(X)) -> U26#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U26# > ok > mark
    
    argument filter:
  
      pi(U26#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U32#(mark(X1),X2) -> U32#(X1,X2)
p2: U32#(ok(X1),ok(X2)) -> U32#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U32# > ok > mark
    
    argument filter:
  
      pi(U32#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U32#(mark(X1),X2) -> U32#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U32#(mark(X1),X2) -> U32#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U32#
    
    argument filter:
  
      pi(U32#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U33#(mark(X)) -> U33#(X)
p2: U33#(ok(X)) -> U33#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U33# > ok > mark
    
    argument filter:
  
      pi(U33#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: isQid#(ok(X)) -> isQid#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      ok > isQid#
    
    argument filter:
  
      pi(isQid#) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
p2: U42#(ok(X1),ok(X2),ok(X3)) -> U42#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U42# > ok > mark
    
    argument filter:
  
      pi(U42#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U42# > mark
    
    argument filter:
  
      pi(U42#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
p2: U43#(ok(X1),ok(X2),ok(X3)) -> U43#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U43# > ok > mark
    
    argument filter:
  
      pi(U43#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U43# > mark
    
    argument filter:
  
      pi(U43#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
p2: U44#(ok(X1),ok(X2),ok(X3)) -> U44#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U44# > ok > mark
    
    argument filter:
  
      pi(U44#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U44# > mark
    
    argument filter:
  
      pi(U44#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U45#(mark(X1),X2) -> U45#(X1,X2)
p2: U45#(ok(X1),ok(X2)) -> U45#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U45# > ok > mark
    
    argument filter:
  
      pi(U45#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U45#(mark(X1),X2) -> U45#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U45#(mark(X1),X2) -> U45#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U45#
    
    argument filter:
  
      pi(U45#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U46#(mark(X)) -> U46#(X)
p2: U46#(ok(X)) -> U46#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U46# > ok > mark
    
    argument filter:
  
      pi(U46#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3)
p2: U52#(ok(X1),ok(X2),ok(X3)) -> U52#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U52# > ok > mark
    
    argument filter:
  
      pi(U52#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U52# > mark
    
    argument filter:
  
      pi(U52#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3)
p2: U53#(ok(X1),ok(X2),ok(X3)) -> U53#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U53# > ok > mark
    
    argument filter:
  
      pi(U53#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U53# > mark
    
    argument filter:
  
      pi(U53#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3)
p2: U54#(ok(X1),ok(X2),ok(X3)) -> U54#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U54# > ok > mark
    
    argument filter:
  
      pi(U54#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U54# > mark
    
    argument filter:
  
      pi(U54#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U55#(mark(X1),X2) -> U55#(X1,X2)
p2: U55#(ok(X1),ok(X2)) -> U55#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U55# > ok > mark
    
    argument filter:
  
      pi(U55#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U55#(mark(X1),X2) -> U55#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U55#(mark(X1),X2) -> U55#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U55#
    
    argument filter:
  
      pi(U55#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U56#(mark(X)) -> U56#(X)
p2: U56#(ok(X)) -> U56#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U56# > ok > mark
    
    argument filter:
  
      pi(U56#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U62#(mark(X1),X2) -> U62#(X1,X2)
p2: U62#(ok(X1),ok(X2)) -> U62#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U62# > ok > mark
    
    argument filter:
  
      pi(U62#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U62#(mark(X1),X2) -> U62#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U62#(mark(X1),X2) -> U62#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U62#
    
    argument filter:
  
      pi(U62#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U63#(mark(X)) -> U63#(X)
p2: U63#(ok(X)) -> U63#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U63# > ok > mark
    
    argument filter:
  
      pi(U63#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U72#(mark(X1),X2) -> U72#(X1,X2)
p2: U72#(ok(X1),ok(X2)) -> U72#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U72# > ok > mark
    
    argument filter:
  
      pi(U72#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U72#(mark(X1),X2) -> U72#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U72#(mark(X1),X2) -> U72#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U72#
    
    argument filter:
  
      pi(U72#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U73#(mark(X1),X2) -> U73#(X1,X2)
p2: U73#(ok(X1),ok(X2)) -> U73#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U73# > ok > mark
    
    argument filter:
  
      pi(U73#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U73#(mark(X1),X2) -> U73#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U73#(mark(X1),X2) -> U73#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U73#
    
    argument filter:
  
      pi(U73#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: isPal#(ok(X)) -> isPal#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      ok > isPal#
    
    argument filter:
  
      pi(isPal#) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U74#(mark(X)) -> U74#(X)
p2: U74#(ok(X)) -> U74#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U74# > ok > mark
    
    argument filter:
  
      pi(U74#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U82#(mark(X1),X2) -> U82#(X1,X2)
p2: U82#(ok(X1),ok(X2)) -> U82#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U82# > ok > mark
    
    argument filter:
  
      pi(U82#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U82#(mark(X1),X2) -> U82#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U82#(mark(X1),X2) -> U82#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U82#
    
    argument filter:
  
      pi(U82#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U83#(mark(X)) -> U83#(X)
p2: U83#(ok(X)) -> U83#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U83# > ok > mark
    
    argument filter:
  
      pi(U83#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: isNePal#(ok(X)) -> isNePal#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      ok > isNePal#
    
    argument filter:
  
      pi(isNePal#) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U92#(mark(X)) -> U92#(X)
p2: U92#(ok(X)) -> U92#(X)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U92# > ok > mark
    
    argument filter:
  
      pi(U92#) = 1
      pi(mark) = [1]
      pi(ok) = [1]

The next rules are strictly ordered:

  p1, p2
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U11#(mark(X1),X2) -> U11#(X1,X2)
p2: U11#(ok(X1),ok(X2)) -> U11#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U11# > ok > mark
    
    argument filter:
  
      pi(U11#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U11#(mark(X1),X2) -> U11#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U11#(mark(X1),X2) -> U11#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U11#
    
    argument filter:
  
      pi(U11#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
p2: U21#(ok(X1),ok(X2),ok(X3)) -> U21#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U21# > ok > mark
    
    argument filter:
  
      pi(U21#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U21# > mark
    
    argument filter:
  
      pi(U21#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U31#(mark(X1),X2) -> U31#(X1,X2)
p2: U31#(ok(X1),ok(X2)) -> U31#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U31# > ok > mark
    
    argument filter:
  
      pi(U31#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U31#(mark(X1),X2) -> U31#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U31#(mark(X1),X2) -> U31#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U31#
    
    argument filter:
  
      pi(U31#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
p2: U41#(ok(X1),ok(X2),ok(X3)) -> U41#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U41# > ok > mark
    
    argument filter:
  
      pi(U41#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U41# > mark
    
    argument filter:
  
      pi(U41#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
p2: U51#(ok(X1),ok(X2),ok(X3)) -> U51#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U51# > ok > mark
    
    argument filter:
  
      pi(U51#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U51# > mark
    
    argument filter:
  
      pi(U51#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U61#(mark(X1),X2) -> U61#(X1,X2)
p2: U61#(ok(X1),ok(X2)) -> U61#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U61# > ok > mark
    
    argument filter:
  
      pi(U61#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U61#(mark(X1),X2) -> U61#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U61#(mark(X1),X2) -> U61#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U61#
    
    argument filter:
  
      pi(U61#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3)
p2: U71#(ok(X1),ok(X2),ok(X3)) -> U71#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U71# > ok > mark
    
    argument filter:
  
      pi(U71#) = 3
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U71# > mark
    
    argument filter:
  
      pi(U71#) = [1]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U81#(mark(X1),X2) -> U81#(X1,X2)
p2: U81#(ok(X1),ok(X2)) -> U81#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U81# > ok > mark
    
    argument filter:
  
      pi(U81#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U81#(mark(X1),X2) -> U81#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U81#(mark(X1),X2) -> U81#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U81#
    
    argument filter:
  
      pi(U81#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.

-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U91#(mark(X1),X2) -> U91#(X1,X2)
p2: U91#(ok(X1),ok(X2)) -> U91#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U91# > ok > mark
    
    argument filter:
  
      pi(U91#) = 2
      pi(mark) = []
      pi(ok) = [1]

The next rules are strictly ordered:

  p2

We remove them from the problem.

-- SCC decomposition.

Consider the dependency pair problem (P, R), where P consists of

p1: U91#(mark(X1),X2) -> U91#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The estimated dependency graph contains the following SCCs:

  {p1}


-- Reduction pair.

Consider the dependency pair problem (P, R), where P consists of

p1: U91#(mark(X1),X2) -> U91#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isPalListKind(V),V))
r5: active(U12(tt(),V)) -> mark(U13(isNeList(V)))
r6: active(U13(tt())) -> mark(tt())
r7: active(U21(tt(),V1,V2)) -> mark(U22(isPalListKind(V1),V1,V2))
r8: active(U22(tt(),V1,V2)) -> mark(U23(isPalListKind(V2),V1,V2))
r9: active(U23(tt(),V1,V2)) -> mark(U24(isPalListKind(V2),V1,V2))
r10: active(U24(tt(),V1,V2)) -> mark(U25(isList(V1),V2))
r11: active(U25(tt(),V2)) -> mark(U26(isList(V2)))
r12: active(U26(tt())) -> mark(tt())
r13: active(U31(tt(),V)) -> mark(U32(isPalListKind(V),V))
r14: active(U32(tt(),V)) -> mark(U33(isQid(V)))
r15: active(U33(tt())) -> mark(tt())
r16: active(U41(tt(),V1,V2)) -> mark(U42(isPalListKind(V1),V1,V2))
r17: active(U42(tt(),V1,V2)) -> mark(U43(isPalListKind(V2),V1,V2))
r18: active(U43(tt(),V1,V2)) -> mark(U44(isPalListKind(V2),V1,V2))
r19: active(U44(tt(),V1,V2)) -> mark(U45(isList(V1),V2))
r20: active(U45(tt(),V2)) -> mark(U46(isNeList(V2)))
r21: active(U46(tt())) -> mark(tt())
r22: active(U51(tt(),V1,V2)) -> mark(U52(isPalListKind(V1),V1,V2))
r23: active(U52(tt(),V1,V2)) -> mark(U53(isPalListKind(V2),V1,V2))
r24: active(U53(tt(),V1,V2)) -> mark(U54(isPalListKind(V2),V1,V2))
r25: active(U54(tt(),V1,V2)) -> mark(U55(isNeList(V1),V2))
r26: active(U55(tt(),V2)) -> mark(U56(isList(V2)))
r27: active(U56(tt())) -> mark(tt())
r28: active(U61(tt(),V)) -> mark(U62(isPalListKind(V),V))
r29: active(U62(tt(),V)) -> mark(U63(isQid(V)))
r30: active(U63(tt())) -> mark(tt())
r31: active(U71(tt(),I,P)) -> mark(U72(isPalListKind(I),P))
r32: active(U72(tt(),P)) -> mark(U73(isPal(P),P))
r33: active(U73(tt(),P)) -> mark(U74(isPalListKind(P)))
r34: active(U74(tt())) -> mark(tt())
r35: active(U81(tt(),V)) -> mark(U82(isPalListKind(V),V))
r36: active(U82(tt(),V)) -> mark(U83(isNePal(V)))
r37: active(U83(tt())) -> mark(tt())
r38: active(U91(tt(),V2)) -> mark(U92(isPalListKind(V2)))
r39: active(U92(tt())) -> mark(tt())
r40: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r41: active(isList(nil())) -> mark(tt())
r42: active(isList(__(V1,V2))) -> mark(U21(isPalListKind(V1),V1,V2))
r43: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r44: active(isNeList(__(V1,V2))) -> mark(U41(isPalListKind(V1),V1,V2))
r45: active(isNeList(__(V1,V2))) -> mark(U51(isPalListKind(V1),V1,V2))
r46: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r47: active(isNePal(__(I,__(P,I)))) -> mark(U71(isQid(I),I,P))
r48: active(isPal(V)) -> mark(U81(isPalListKind(V),V))
r49: active(isPal(nil())) -> mark(tt())
r50: active(isPalListKind(a())) -> mark(tt())
r51: active(isPalListKind(e())) -> mark(tt())
r52: active(isPalListKind(i())) -> mark(tt())
r53: active(isPalListKind(nil())) -> mark(tt())
r54: active(isPalListKind(o())) -> mark(tt())
r55: active(isPalListKind(u())) -> mark(tt())
r56: active(isPalListKind(__(V1,V2))) -> mark(U91(isPalListKind(V1),V2))
r57: active(isQid(a())) -> mark(tt())
r58: active(isQid(e())) -> mark(tt())
r59: active(isQid(i())) -> mark(tt())
r60: active(isQid(o())) -> mark(tt())
r61: active(isQid(u())) -> mark(tt())
r62: active(__(X1,X2)) -> __(active(X1),X2)
r63: active(__(X1,X2)) -> __(X1,active(X2))
r64: active(U11(X1,X2)) -> U11(active(X1),X2)
r65: active(U12(X1,X2)) -> U12(active(X1),X2)
r66: active(U13(X)) -> U13(active(X))
r67: active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
r68: active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
r69: active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
r70: active(U24(X1,X2,X3)) -> U24(active(X1),X2,X3)
r71: active(U25(X1,X2)) -> U25(active(X1),X2)
r72: active(U26(X)) -> U26(active(X))
r73: active(U31(X1,X2)) -> U31(active(X1),X2)
r74: active(U32(X1,X2)) -> U32(active(X1),X2)
r75: active(U33(X)) -> U33(active(X))
r76: active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
r77: active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
r78: active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
r79: active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
r80: active(U45(X1,X2)) -> U45(active(X1),X2)
r81: active(U46(X)) -> U46(active(X))
r82: active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
r83: active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
r84: active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
r85: active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
r86: active(U55(X1,X2)) -> U55(active(X1),X2)
r87: active(U56(X)) -> U56(active(X))
r88: active(U61(X1,X2)) -> U61(active(X1),X2)
r89: active(U62(X1,X2)) -> U62(active(X1),X2)
r90: active(U63(X)) -> U63(active(X))
r91: active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
r92: active(U72(X1,X2)) -> U72(active(X1),X2)
r93: active(U73(X1,X2)) -> U73(active(X1),X2)
r94: active(U74(X)) -> U74(active(X))
r95: active(U81(X1,X2)) -> U81(active(X1),X2)
r96: active(U82(X1,X2)) -> U82(active(X1),X2)
r97: active(U83(X)) -> U83(active(X))
r98: active(U91(X1,X2)) -> U91(active(X1),X2)
r99: active(U92(X)) -> U92(active(X))
r100: __(mark(X1),X2) -> mark(__(X1,X2))
r101: __(X1,mark(X2)) -> mark(__(X1,X2))
r102: U11(mark(X1),X2) -> mark(U11(X1,X2))
r103: U12(mark(X1),X2) -> mark(U12(X1,X2))
r104: U13(mark(X)) -> mark(U13(X))
r105: U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
r106: U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
r107: U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
r108: U24(mark(X1),X2,X3) -> mark(U24(X1,X2,X3))
r109: U25(mark(X1),X2) -> mark(U25(X1,X2))
r110: U26(mark(X)) -> mark(U26(X))
r111: U31(mark(X1),X2) -> mark(U31(X1,X2))
r112: U32(mark(X1),X2) -> mark(U32(X1,X2))
r113: U33(mark(X)) -> mark(U33(X))
r114: U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
r115: U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
r116: U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
r117: U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
r118: U45(mark(X1),X2) -> mark(U45(X1,X2))
r119: U46(mark(X)) -> mark(U46(X))
r120: U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
r121: U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
r122: U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
r123: U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
r124: U55(mark(X1),X2) -> mark(U55(X1,X2))
r125: U56(mark(X)) -> mark(U56(X))
r126: U61(mark(X1),X2) -> mark(U61(X1,X2))
r127: U62(mark(X1),X2) -> mark(U62(X1,X2))
r128: U63(mark(X)) -> mark(U63(X))
r129: U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
r130: U72(mark(X1),X2) -> mark(U72(X1,X2))
r131: U73(mark(X1),X2) -> mark(U73(X1,X2))
r132: U74(mark(X)) -> mark(U74(X))
r133: U81(mark(X1),X2) -> mark(U81(X1,X2))
r134: U82(mark(X1),X2) -> mark(U82(X1,X2))
r135: U83(mark(X)) -> mark(U83(X))
r136: U91(mark(X1),X2) -> mark(U91(X1,X2))
r137: U92(mark(X)) -> mark(U92(X))
r138: proper(__(X1,X2)) -> __(proper(X1),proper(X2))
r139: proper(nil()) -> ok(nil())
r140: proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
r141: proper(tt()) -> ok(tt())
r142: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
r143: proper(isPalListKind(X)) -> isPalListKind(proper(X))
r144: proper(U13(X)) -> U13(proper(X))
r145: proper(isNeList(X)) -> isNeList(proper(X))
r146: proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
r147: proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
r148: proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
r149: proper(U24(X1,X2,X3)) -> U24(proper(X1),proper(X2),proper(X3))
r150: proper(U25(X1,X2)) -> U25(proper(X1),proper(X2))
r151: proper(isList(X)) -> isList(proper(X))
r152: proper(U26(X)) -> U26(proper(X))
r153: proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
r154: proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
r155: proper(U33(X)) -> U33(proper(X))
r156: proper(isQid(X)) -> isQid(proper(X))
r157: proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
r158: proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
r159: proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
r160: proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
r161: proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
r162: proper(U46(X)) -> U46(proper(X))
r163: proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
r164: proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
r165: proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
r166: proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
r167: proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
r168: proper(U56(X)) -> U56(proper(X))
r169: proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
r170: proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
r171: proper(U63(X)) -> U63(proper(X))
r172: proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
r173: proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
r174: proper(U73(X1,X2)) -> U73(proper(X1),proper(X2))
r175: proper(isPal(X)) -> isPal(proper(X))
r176: proper(U74(X)) -> U74(proper(X))
r177: proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
r178: proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
r179: proper(U83(X)) -> U83(proper(X))
r180: proper(isNePal(X)) -> isNePal(proper(X))
r181: proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
r182: proper(U92(X)) -> U92(proper(X))
r183: proper(a()) -> ok(a())
r184: proper(e()) -> ok(e())
r185: proper(i()) -> ok(i())
r186: proper(o()) -> ok(o())
r187: proper(u()) -> ok(u())
r188: __(ok(X1),ok(X2)) -> ok(__(X1,X2))
r189: U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
r190: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
r191: isPalListKind(ok(X)) -> ok(isPalListKind(X))
r192: U13(ok(X)) -> ok(U13(X))
r193: isNeList(ok(X)) -> ok(isNeList(X))
r194: U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
r195: U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
r196: U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
r197: U24(ok(X1),ok(X2),ok(X3)) -> ok(U24(X1,X2,X3))
r198: U25(ok(X1),ok(X2)) -> ok(U25(X1,X2))
r199: isList(ok(X)) -> ok(isList(X))
r200: U26(ok(X)) -> ok(U26(X))
r201: U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
r202: U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
r203: U33(ok(X)) -> ok(U33(X))
r204: isQid(ok(X)) -> ok(isQid(X))
r205: U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
r206: U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
r207: U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
r208: U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
r209: U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
r210: U46(ok(X)) -> ok(U46(X))
r211: U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
r212: U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
r213: U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
r214: U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
r215: U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
r216: U56(ok(X)) -> ok(U56(X))
r217: U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
r218: U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
r219: U63(ok(X)) -> ok(U63(X))
r220: U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
r221: U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
r222: U73(ok(X1),ok(X2)) -> ok(U73(X1,X2))
r223: isPal(ok(X)) -> ok(isPal(X))
r224: U74(ok(X)) -> ok(U74(X))
r225: U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
r226: U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
r227: U83(ok(X)) -> ok(U83(X))
r228: isNePal(ok(X)) -> ok(isNePal(X))
r229: U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
r230: U92(ok(X)) -> ok(U92(X))
r231: top(mark(X)) -> top(proper(X))
r232: top(ok(X)) -> top(active(X))

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark > U91#
    
    argument filter:
  
      pi(U91#) = [1, 2]
      pi(mark) = [1]

The next rules are strictly ordered:

  p1
  r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, r232

We remove them from the problem.  Then no dependency pair remains.