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

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: active#(__(__(X,Y),Z)) -> __#(X,__(Y,Z))
p3: active#(__(__(X,Y),Z)) -> __#(Y,Z)
p4: active#(__(X,nil())) -> mark#(X)
p5: active#(__(nil(),X)) -> mark#(X)
p6: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p7: active#(U11(tt(),V)) -> U12#(isPalListKind(V),V)
p8: active#(U11(tt(),V)) -> isPalListKind#(V)
p9: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p10: active#(U12(tt(),V)) -> U13#(isNeList(V))
p11: active#(U12(tt(),V)) -> isNeList#(V)
p12: active#(U13(tt())) -> mark#(tt())
p13: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p14: active#(U21(tt(),V1,V2)) -> U22#(isPalListKind(V1),V1,V2)
p15: active#(U21(tt(),V1,V2)) -> isPalListKind#(V1)
p16: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p17: active#(U22(tt(),V1,V2)) -> U23#(isPalListKind(V2),V1,V2)
p18: active#(U22(tt(),V1,V2)) -> isPalListKind#(V2)
p19: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p20: active#(U23(tt(),V1,V2)) -> U24#(isPalListKind(V2),V1,V2)
p21: active#(U23(tt(),V1,V2)) -> isPalListKind#(V2)
p22: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p23: active#(U24(tt(),V1,V2)) -> U25#(isList(V1),V2)
p24: active#(U24(tt(),V1,V2)) -> isList#(V1)
p25: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p26: active#(U25(tt(),V2)) -> U26#(isList(V2))
p27: active#(U25(tt(),V2)) -> isList#(V2)
p28: active#(U26(tt())) -> mark#(tt())
p29: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p30: active#(U31(tt(),V)) -> U32#(isPalListKind(V),V)
p31: active#(U31(tt(),V)) -> isPalListKind#(V)
p32: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p33: active#(U32(tt(),V)) -> U33#(isQid(V))
p34: active#(U32(tt(),V)) -> isQid#(V)
p35: active#(U33(tt())) -> mark#(tt())
p36: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p37: active#(U41(tt(),V1,V2)) -> U42#(isPalListKind(V1),V1,V2)
p38: active#(U41(tt(),V1,V2)) -> isPalListKind#(V1)
p39: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p40: active#(U42(tt(),V1,V2)) -> U43#(isPalListKind(V2),V1,V2)
p41: active#(U42(tt(),V1,V2)) -> isPalListKind#(V2)
p42: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p43: active#(U43(tt(),V1,V2)) -> U44#(isPalListKind(V2),V1,V2)
p44: active#(U43(tt(),V1,V2)) -> isPalListKind#(V2)
p45: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p46: active#(U44(tt(),V1,V2)) -> U45#(isList(V1),V2)
p47: active#(U44(tt(),V1,V2)) -> isList#(V1)
p48: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p49: active#(U45(tt(),V2)) -> U46#(isNeList(V2))
p50: active#(U45(tt(),V2)) -> isNeList#(V2)
p51: active#(U46(tt())) -> mark#(tt())
p52: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p53: active#(U51(tt(),V1,V2)) -> U52#(isPalListKind(V1),V1,V2)
p54: active#(U51(tt(),V1,V2)) -> isPalListKind#(V1)
p55: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p56: active#(U52(tt(),V1,V2)) -> U53#(isPalListKind(V2),V1,V2)
p57: active#(U52(tt(),V1,V2)) -> isPalListKind#(V2)
p58: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p59: active#(U53(tt(),V1,V2)) -> U54#(isPalListKind(V2),V1,V2)
p60: active#(U53(tt(),V1,V2)) -> isPalListKind#(V2)
p61: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p62: active#(U54(tt(),V1,V2)) -> U55#(isNeList(V1),V2)
p63: active#(U54(tt(),V1,V2)) -> isNeList#(V1)
p64: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p65: active#(U55(tt(),V2)) -> U56#(isList(V2))
p66: active#(U55(tt(),V2)) -> isList#(V2)
p67: active#(U56(tt())) -> mark#(tt())
p68: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p69: active#(U61(tt(),V)) -> U62#(isPalListKind(V),V)
p70: active#(U61(tt(),V)) -> isPalListKind#(V)
p71: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p72: active#(U62(tt(),V)) -> U63#(isQid(V))
p73: active#(U62(tt(),V)) -> isQid#(V)
p74: active#(U63(tt())) -> mark#(tt())
p75: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p76: active#(U71(tt(),I,P)) -> U72#(isPalListKind(I),P)
p77: active#(U71(tt(),I,P)) -> isPalListKind#(I)
p78: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p79: active#(U72(tt(),P)) -> U73#(isPal(P),P)
p80: active#(U72(tt(),P)) -> isPal#(P)
p81: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p82: active#(U73(tt(),P)) -> U74#(isPalListKind(P))
p83: active#(U73(tt(),P)) -> isPalListKind#(P)
p84: active#(U74(tt())) -> mark#(tt())
p85: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p86: active#(U81(tt(),V)) -> U82#(isPalListKind(V),V)
p87: active#(U81(tt(),V)) -> isPalListKind#(V)
p88: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p89: active#(U82(tt(),V)) -> U83#(isNePal(V))
p90: active#(U82(tt(),V)) -> isNePal#(V)
p91: active#(U83(tt())) -> mark#(tt())
p92: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p93: active#(U91(tt(),V2)) -> U92#(isPalListKind(V2))
p94: active#(U91(tt(),V2)) -> isPalListKind#(V2)
p95: active#(U92(tt())) -> mark#(tt())
p96: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p97: active#(isList(V)) -> U11#(isPalListKind(V),V)
p98: active#(isList(V)) -> isPalListKind#(V)
p99: active#(isList(nil())) -> mark#(tt())
p100: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p101: active#(isList(__(V1,V2))) -> U21#(isPalListKind(V1),V1,V2)
p102: active#(isList(__(V1,V2))) -> isPalListKind#(V1)
p103: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p104: active#(isNeList(V)) -> U31#(isPalListKind(V),V)
p105: active#(isNeList(V)) -> isPalListKind#(V)
p106: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p107: active#(isNeList(__(V1,V2))) -> U41#(isPalListKind(V1),V1,V2)
p108: active#(isNeList(__(V1,V2))) -> isPalListKind#(V1)
p109: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p110: active#(isNeList(__(V1,V2))) -> U51#(isPalListKind(V1),V1,V2)
p111: active#(isNeList(__(V1,V2))) -> isPalListKind#(V1)
p112: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p113: active#(isNePal(V)) -> U61#(isPalListKind(V),V)
p114: active#(isNePal(V)) -> isPalListKind#(V)
p115: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p116: active#(isNePal(__(I,__(P,I)))) -> U71#(isQid(I),I,P)
p117: active#(isNePal(__(I,__(P,I)))) -> isQid#(I)
p118: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p119: active#(isPal(V)) -> U81#(isPalListKind(V),V)
p120: active#(isPal(V)) -> isPalListKind#(V)
p121: active#(isPal(nil())) -> mark#(tt())
p122: active#(isPalListKind(a())) -> mark#(tt())
p123: active#(isPalListKind(e())) -> mark#(tt())
p124: active#(isPalListKind(i())) -> mark#(tt())
p125: active#(isPalListKind(nil())) -> mark#(tt())
p126: active#(isPalListKind(o())) -> mark#(tt())
p127: active#(isPalListKind(u())) -> mark#(tt())
p128: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p129: active#(isPalListKind(__(V1,V2))) -> U91#(isPalListKind(V1),V2)
p130: active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1)
p131: active#(isQid(a())) -> mark#(tt())
p132: active#(isQid(e())) -> mark#(tt())
p133: active#(isQid(i())) -> mark#(tt())
p134: active#(isQid(o())) -> mark#(tt())
p135: active#(isQid(u())) -> mark#(tt())
p136: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p137: mark#(__(X1,X2)) -> __#(mark(X1),mark(X2))
p138: mark#(__(X1,X2)) -> mark#(X1)
p139: mark#(__(X1,X2)) -> mark#(X2)
p140: mark#(nil()) -> active#(nil())
p141: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p142: mark#(U11(X1,X2)) -> U11#(mark(X1),X2)
p143: mark#(U11(X1,X2)) -> mark#(X1)
p144: mark#(tt()) -> active#(tt())
p145: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p146: mark#(U12(X1,X2)) -> U12#(mark(X1),X2)
p147: mark#(U12(X1,X2)) -> mark#(X1)
p148: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p149: mark#(U13(X)) -> active#(U13(mark(X)))
p150: mark#(U13(X)) -> U13#(mark(X))
p151: mark#(U13(X)) -> mark#(X)
p152: mark#(isNeList(X)) -> active#(isNeList(X))
p153: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p154: mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3)
p155: mark#(U21(X1,X2,X3)) -> mark#(X1)
p156: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p157: mark#(U22(X1,X2,X3)) -> U22#(mark(X1),X2,X3)
p158: mark#(U22(X1,X2,X3)) -> mark#(X1)
p159: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p160: mark#(U23(X1,X2,X3)) -> U23#(mark(X1),X2,X3)
p161: mark#(U23(X1,X2,X3)) -> mark#(X1)
p162: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p163: mark#(U24(X1,X2,X3)) -> U24#(mark(X1),X2,X3)
p164: mark#(U24(X1,X2,X3)) -> mark#(X1)
p165: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p166: mark#(U25(X1,X2)) -> U25#(mark(X1),X2)
p167: mark#(U25(X1,X2)) -> mark#(X1)
p168: mark#(isList(X)) -> active#(isList(X))
p169: mark#(U26(X)) -> active#(U26(mark(X)))
p170: mark#(U26(X)) -> U26#(mark(X))
p171: mark#(U26(X)) -> mark#(X)
p172: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p173: mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
p174: mark#(U31(X1,X2)) -> mark#(X1)
p175: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p176: mark#(U32(X1,X2)) -> U32#(mark(X1),X2)
p177: mark#(U32(X1,X2)) -> mark#(X1)
p178: mark#(U33(X)) -> active#(U33(mark(X)))
p179: mark#(U33(X)) -> U33#(mark(X))
p180: mark#(U33(X)) -> mark#(X)
p181: mark#(isQid(X)) -> active#(isQid(X))
p182: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p183: mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
p184: mark#(U41(X1,X2,X3)) -> mark#(X1)
p185: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p186: mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3)
p187: mark#(U42(X1,X2,X3)) -> mark#(X1)
p188: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p189: mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3)
p190: mark#(U43(X1,X2,X3)) -> mark#(X1)
p191: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p192: mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3)
p193: mark#(U44(X1,X2,X3)) -> mark#(X1)
p194: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p195: mark#(U45(X1,X2)) -> U45#(mark(X1),X2)
p196: mark#(U45(X1,X2)) -> mark#(X1)
p197: mark#(U46(X)) -> active#(U46(mark(X)))
p198: mark#(U46(X)) -> U46#(mark(X))
p199: mark#(U46(X)) -> mark#(X)
p200: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p201: mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
p202: mark#(U51(X1,X2,X3)) -> mark#(X1)
p203: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p204: mark#(U52(X1,X2,X3)) -> U52#(mark(X1),X2,X3)
p205: mark#(U52(X1,X2,X3)) -> mark#(X1)
p206: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p207: mark#(U53(X1,X2,X3)) -> U53#(mark(X1),X2,X3)
p208: mark#(U53(X1,X2,X3)) -> mark#(X1)
p209: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p210: mark#(U54(X1,X2,X3)) -> U54#(mark(X1),X2,X3)
p211: mark#(U54(X1,X2,X3)) -> mark#(X1)
p212: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p213: mark#(U55(X1,X2)) -> U55#(mark(X1),X2)
p214: mark#(U55(X1,X2)) -> mark#(X1)
p215: mark#(U56(X)) -> active#(U56(mark(X)))
p216: mark#(U56(X)) -> U56#(mark(X))
p217: mark#(U56(X)) -> mark#(X)
p218: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p219: mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
p220: mark#(U61(X1,X2)) -> mark#(X1)
p221: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p222: mark#(U62(X1,X2)) -> U62#(mark(X1),X2)
p223: mark#(U62(X1,X2)) -> mark#(X1)
p224: mark#(U63(X)) -> active#(U63(mark(X)))
p225: mark#(U63(X)) -> U63#(mark(X))
p226: mark#(U63(X)) -> mark#(X)
p227: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p228: mark#(U71(X1,X2,X3)) -> U71#(mark(X1),X2,X3)
p229: mark#(U71(X1,X2,X3)) -> mark#(X1)
p230: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p231: mark#(U72(X1,X2)) -> U72#(mark(X1),X2)
p232: mark#(U72(X1,X2)) -> mark#(X1)
p233: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p234: mark#(U73(X1,X2)) -> U73#(mark(X1),X2)
p235: mark#(U73(X1,X2)) -> mark#(X1)
p236: mark#(isPal(X)) -> active#(isPal(X))
p237: mark#(U74(X)) -> active#(U74(mark(X)))
p238: mark#(U74(X)) -> U74#(mark(X))
p239: mark#(U74(X)) -> mark#(X)
p240: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p241: mark#(U81(X1,X2)) -> U81#(mark(X1),X2)
p242: mark#(U81(X1,X2)) -> mark#(X1)
p243: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p244: mark#(U82(X1,X2)) -> U82#(mark(X1),X2)
p245: mark#(U82(X1,X2)) -> mark#(X1)
p246: mark#(U83(X)) -> active#(U83(mark(X)))
p247: mark#(U83(X)) -> U83#(mark(X))
p248: mark#(U83(X)) -> mark#(X)
p249: mark#(isNePal(X)) -> active#(isNePal(X))
p250: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p251: mark#(U91(X1,X2)) -> U91#(mark(X1),X2)
p252: mark#(U91(X1,X2)) -> mark#(X1)
p253: mark#(U92(X)) -> active#(U92(mark(X)))
p254: mark#(U92(X)) -> U92#(mark(X))
p255: mark#(U92(X)) -> mark#(X)
p256: mark#(a()) -> active#(a())
p257: mark#(e()) -> active#(e())
p258: mark#(i()) -> active#(i())
p259: mark#(o()) -> active#(o())
p260: mark#(u()) -> active#(u())
p261: __#(mark(X1),X2) -> __#(X1,X2)
p262: __#(X1,mark(X2)) -> __#(X1,X2)
p263: __#(active(X1),X2) -> __#(X1,X2)
p264: __#(X1,active(X2)) -> __#(X1,X2)
p265: U11#(mark(X1),X2) -> U11#(X1,X2)
p266: U11#(X1,mark(X2)) -> U11#(X1,X2)
p267: U11#(active(X1),X2) -> U11#(X1,X2)
p268: U11#(X1,active(X2)) -> U11#(X1,X2)
p269: U12#(mark(X1),X2) -> U12#(X1,X2)
p270: U12#(X1,mark(X2)) -> U12#(X1,X2)
p271: U12#(active(X1),X2) -> U12#(X1,X2)
p272: U12#(X1,active(X2)) -> U12#(X1,X2)
p273: isPalListKind#(mark(X)) -> isPalListKind#(X)
p274: isPalListKind#(active(X)) -> isPalListKind#(X)
p275: U13#(mark(X)) -> U13#(X)
p276: U13#(active(X)) -> U13#(X)
p277: isNeList#(mark(X)) -> isNeList#(X)
p278: isNeList#(active(X)) -> isNeList#(X)
p279: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
p280: U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
p281: U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
p282: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
p283: U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
p284: U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
p285: U22#(mark(X1),X2,X3) -> U22#(X1,X2,X3)
p286: U22#(X1,mark(X2),X3) -> U22#(X1,X2,X3)
p287: U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3)
p288: U22#(active(X1),X2,X3) -> U22#(X1,X2,X3)
p289: U22#(X1,active(X2),X3) -> U22#(X1,X2,X3)
p290: U22#(X1,X2,active(X3)) -> U22#(X1,X2,X3)
p291: U23#(mark(X1),X2,X3) -> U23#(X1,X2,X3)
p292: U23#(X1,mark(X2),X3) -> U23#(X1,X2,X3)
p293: U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3)
p294: U23#(active(X1),X2,X3) -> U23#(X1,X2,X3)
p295: U23#(X1,active(X2),X3) -> U23#(X1,X2,X3)
p296: U23#(X1,X2,active(X3)) -> U23#(X1,X2,X3)
p297: U24#(mark(X1),X2,X3) -> U24#(X1,X2,X3)
p298: U24#(X1,mark(X2),X3) -> U24#(X1,X2,X3)
p299: U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3)
p300: U24#(active(X1),X2,X3) -> U24#(X1,X2,X3)
p301: U24#(X1,active(X2),X3) -> U24#(X1,X2,X3)
p302: U24#(X1,X2,active(X3)) -> U24#(X1,X2,X3)
p303: U25#(mark(X1),X2) -> U25#(X1,X2)
p304: U25#(X1,mark(X2)) -> U25#(X1,X2)
p305: U25#(active(X1),X2) -> U25#(X1,X2)
p306: U25#(X1,active(X2)) -> U25#(X1,X2)
p307: isList#(mark(X)) -> isList#(X)
p308: isList#(active(X)) -> isList#(X)
p309: U26#(mark(X)) -> U26#(X)
p310: U26#(active(X)) -> U26#(X)
p311: U31#(mark(X1),X2) -> U31#(X1,X2)
p312: U31#(X1,mark(X2)) -> U31#(X1,X2)
p313: U31#(active(X1),X2) -> U31#(X1,X2)
p314: U31#(X1,active(X2)) -> U31#(X1,X2)
p315: U32#(mark(X1),X2) -> U32#(X1,X2)
p316: U32#(X1,mark(X2)) -> U32#(X1,X2)
p317: U32#(active(X1),X2) -> U32#(X1,X2)
p318: U32#(X1,active(X2)) -> U32#(X1,X2)
p319: U33#(mark(X)) -> U33#(X)
p320: U33#(active(X)) -> U33#(X)
p321: isQid#(mark(X)) -> isQid#(X)
p322: isQid#(active(X)) -> isQid#(X)
p323: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
p324: U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
p325: U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
p326: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
p327: U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
p328: U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
p329: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3)
p330: U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3)
p331: U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3)
p332: U42#(active(X1),X2,X3) -> U42#(X1,X2,X3)
p333: U42#(X1,active(X2),X3) -> U42#(X1,X2,X3)
p334: U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3)
p335: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3)
p336: U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3)
p337: U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3)
p338: U43#(active(X1),X2,X3) -> U43#(X1,X2,X3)
p339: U43#(X1,active(X2),X3) -> U43#(X1,X2,X3)
p340: U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3)
p341: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3)
p342: U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3)
p343: U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3)
p344: U44#(active(X1),X2,X3) -> U44#(X1,X2,X3)
p345: U44#(X1,active(X2),X3) -> U44#(X1,X2,X3)
p346: U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3)
p347: U45#(mark(X1),X2) -> U45#(X1,X2)
p348: U45#(X1,mark(X2)) -> U45#(X1,X2)
p349: U45#(active(X1),X2) -> U45#(X1,X2)
p350: U45#(X1,active(X2)) -> U45#(X1,X2)
p351: U46#(mark(X)) -> U46#(X)
p352: U46#(active(X)) -> U46#(X)
p353: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
p354: U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
p355: U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
p356: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
p357: U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
p358: U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
p359: U52#(mark(X1),X2,X3) -> U52#(X1,X2,X3)
p360: U52#(X1,mark(X2),X3) -> U52#(X1,X2,X3)
p361: U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3)
p362: U52#(active(X1),X2,X3) -> U52#(X1,X2,X3)
p363: U52#(X1,active(X2),X3) -> U52#(X1,X2,X3)
p364: U52#(X1,X2,active(X3)) -> U52#(X1,X2,X3)
p365: U53#(mark(X1),X2,X3) -> U53#(X1,X2,X3)
p366: U53#(X1,mark(X2),X3) -> U53#(X1,X2,X3)
p367: U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3)
p368: U53#(active(X1),X2,X3) -> U53#(X1,X2,X3)
p369: U53#(X1,active(X2),X3) -> U53#(X1,X2,X3)
p370: U53#(X1,X2,active(X3)) -> U53#(X1,X2,X3)
p371: U54#(mark(X1),X2,X3) -> U54#(X1,X2,X3)
p372: U54#(X1,mark(X2),X3) -> U54#(X1,X2,X3)
p373: U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3)
p374: U54#(active(X1),X2,X3) -> U54#(X1,X2,X3)
p375: U54#(X1,active(X2),X3) -> U54#(X1,X2,X3)
p376: U54#(X1,X2,active(X3)) -> U54#(X1,X2,X3)
p377: U55#(mark(X1),X2) -> U55#(X1,X2)
p378: U55#(X1,mark(X2)) -> U55#(X1,X2)
p379: U55#(active(X1),X2) -> U55#(X1,X2)
p380: U55#(X1,active(X2)) -> U55#(X1,X2)
p381: U56#(mark(X)) -> U56#(X)
p382: U56#(active(X)) -> U56#(X)
p383: U61#(mark(X1),X2) -> U61#(X1,X2)
p384: U61#(X1,mark(X2)) -> U61#(X1,X2)
p385: U61#(active(X1),X2) -> U61#(X1,X2)
p386: U61#(X1,active(X2)) -> U61#(X1,X2)
p387: U62#(mark(X1),X2) -> U62#(X1,X2)
p388: U62#(X1,mark(X2)) -> U62#(X1,X2)
p389: U62#(active(X1),X2) -> U62#(X1,X2)
p390: U62#(X1,active(X2)) -> U62#(X1,X2)
p391: U63#(mark(X)) -> U63#(X)
p392: U63#(active(X)) -> U63#(X)
p393: U71#(mark(X1),X2,X3) -> U71#(X1,X2,X3)
p394: U71#(X1,mark(X2),X3) -> U71#(X1,X2,X3)
p395: U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3)
p396: U71#(active(X1),X2,X3) -> U71#(X1,X2,X3)
p397: U71#(X1,active(X2),X3) -> U71#(X1,X2,X3)
p398: U71#(X1,X2,active(X3)) -> U71#(X1,X2,X3)
p399: U72#(mark(X1),X2) -> U72#(X1,X2)
p400: U72#(X1,mark(X2)) -> U72#(X1,X2)
p401: U72#(active(X1),X2) -> U72#(X1,X2)
p402: U72#(X1,active(X2)) -> U72#(X1,X2)
p403: U73#(mark(X1),X2) -> U73#(X1,X2)
p404: U73#(X1,mark(X2)) -> U73#(X1,X2)
p405: U73#(active(X1),X2) -> U73#(X1,X2)
p406: U73#(X1,active(X2)) -> U73#(X1,X2)
p407: isPal#(mark(X)) -> isPal#(X)
p408: isPal#(active(X)) -> isPal#(X)
p409: U74#(mark(X)) -> U74#(X)
p410: U74#(active(X)) -> U74#(X)
p411: U81#(mark(X1),X2) -> U81#(X1,X2)
p412: U81#(X1,mark(X2)) -> U81#(X1,X2)
p413: U81#(active(X1),X2) -> U81#(X1,X2)
p414: U81#(X1,active(X2)) -> U81#(X1,X2)
p415: U82#(mark(X1),X2) -> U82#(X1,X2)
p416: U82#(X1,mark(X2)) -> U82#(X1,X2)
p417: U82#(active(X1),X2) -> U82#(X1,X2)
p418: U82#(X1,active(X2)) -> U82#(X1,X2)
p419: U83#(mark(X)) -> U83#(X)
p420: U83#(active(X)) -> U83#(X)
p421: isNePal#(mark(X)) -> isNePal#(X)
p422: isNePal#(active(X)) -> isNePal#(X)
p423: U91#(mark(X1),X2) -> U91#(X1,X2)
p424: U91#(X1,mark(X2)) -> U91#(X1,X2)
p425: U91#(active(X1),X2) -> U91#(X1,X2)
p426: U91#(X1,active(X2)) -> U91#(X1,X2)
p427: U92#(mark(X)) -> U92#(X)
p428: U92#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {p1, p4, p5, p6, p9, p13, p16, p19, p22, p25, p29, p32, p36, p39, p42, p45, p48, p52, p55, p58, p61, p64, p68, p71, p75, p78, p81, p85, p88, p92, p96, p100, p103, p106, p109, p112, p115, p118, p128, p136, p138, p139, p141, p143, p145, p147, p148, p149, p151, p152, p153, p155, p156, p158, p159, p161, p162, p164, p165, p167, p168, p169, p171, p172, p174, p175, p177, p178, p180, p181, p182, p184, p185, p187, p188, p190, p191, p193, p194, p196, p197, p199, p200, p202, p203, p205, p206, p208, p209, p211, p212, p214, p215, p217, p218, p220, p221, p223, p224, p226, p227, p229, p230, p232, p233, p235, p236, p237, p239, p240, p242, p243, p245, p246, p248, p249, p250, p252, p253, p255}
  {p261, p262, p263, p264}
  {p269, p270, p271, p272}
  {p273, p274}
  {p275, p276}
  {p277, p278}
  {p285, p286, p287, p288, p289, p290}
  {p291, p292, p293, p294, p295, p296}
  {p297, p298, p299, p300, p301, p302}
  {p303, p304, p305, p306}
  {p307, p308}
  {p309, p310}
  {p315, p316, p317, p318}
  {p319, p320}
  {p321, p322}
  {p329, p330, p331, p332, p333, p334}
  {p335, p336, p337, p338, p339, p340}
  {p341, p342, p343, p344, p345, p346}
  {p347, p348, p349, p350}
  {p351, p352}
  {p359, p360, p361, p362, p363, p364}
  {p365, p366, p367, p368, p369, p370}
  {p371, p372, p373, p374, p375, p376}
  {p377, p378, p379, p380}
  {p381, p382}
  {p387, p388, p389, p390}
  {p391, p392}
  {p399, p400, p401, p402}
  {p403, p404, p405, p406}
  {p407, p408}
  {p409, p410}
  {p415, p416, p417, p418}
  {p419, p420}
  {p421, p422}
  {p427, p428}
  {p265, p266, p267, p268}
  {p279, p280, p281, p282, p283, p284}
  {p311, p312, p313, p314}
  {p323, p324, p325, p326, p327, p328}
  {p353, p354, p355, p356, p357, p358}
  {p383, p384, p385, p386}
  {p393, p394, p395, p396, p397, p398}
  {p411, p412, p413, p414}
  {p423, p424, p425, p426}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: mark#(U92(X)) -> active#(U92(mark(X)))
p4: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p5: mark#(U91(X1,X2)) -> mark#(X1)
p6: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p7: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p8: mark#(isNePal(X)) -> active#(isNePal(X))
p9: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p10: mark#(U83(X)) -> mark#(X)
p11: mark#(U83(X)) -> active#(U83(mark(X)))
p12: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p13: mark#(U82(X1,X2)) -> mark#(X1)
p14: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p15: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p16: mark#(U81(X1,X2)) -> mark#(X1)
p17: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p18: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p19: mark#(U74(X)) -> mark#(X)
p20: mark#(U74(X)) -> active#(U74(mark(X)))
p21: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p22: mark#(isPal(X)) -> active#(isPal(X))
p23: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p24: mark#(U73(X1,X2)) -> mark#(X1)
p25: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p26: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p27: mark#(U72(X1,X2)) -> mark#(X1)
p28: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p29: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p30: mark#(U71(X1,X2,X3)) -> mark#(X1)
p31: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p32: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p33: mark#(U63(X)) -> mark#(X)
p34: mark#(U63(X)) -> active#(U63(mark(X)))
p35: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p36: mark#(U62(X1,X2)) -> mark#(X1)
p37: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p38: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p39: mark#(U61(X1,X2)) -> mark#(X1)
p40: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p41: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p42: mark#(U56(X)) -> mark#(X)
p43: mark#(U56(X)) -> active#(U56(mark(X)))
p44: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p45: mark#(U55(X1,X2)) -> mark#(X1)
p46: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p47: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p48: mark#(U54(X1,X2,X3)) -> mark#(X1)
p49: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p50: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p51: mark#(U53(X1,X2,X3)) -> mark#(X1)
p52: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p53: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p54: mark#(U52(X1,X2,X3)) -> mark#(X1)
p55: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p56: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p57: mark#(U51(X1,X2,X3)) -> mark#(X1)
p58: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p59: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p60: mark#(U46(X)) -> mark#(X)
p61: mark#(U46(X)) -> active#(U46(mark(X)))
p62: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p63: mark#(U45(X1,X2)) -> mark#(X1)
p64: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p65: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p66: mark#(U44(X1,X2,X3)) -> mark#(X1)
p67: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p68: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p69: mark#(U43(X1,X2,X3)) -> mark#(X1)
p70: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p71: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p72: mark#(U42(X1,X2,X3)) -> mark#(X1)
p73: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p74: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p75: mark#(U41(X1,X2,X3)) -> mark#(X1)
p76: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p77: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p78: mark#(isQid(X)) -> active#(isQid(X))
p79: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p80: mark#(U33(X)) -> mark#(X)
p81: mark#(U33(X)) -> active#(U33(mark(X)))
p82: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p83: mark#(U32(X1,X2)) -> mark#(X1)
p84: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p85: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p86: mark#(U31(X1,X2)) -> mark#(X1)
p87: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p88: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p89: mark#(U26(X)) -> mark#(X)
p90: mark#(U26(X)) -> active#(U26(mark(X)))
p91: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p92: mark#(isList(X)) -> active#(isList(X))
p93: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p94: mark#(U25(X1,X2)) -> mark#(X1)
p95: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p96: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p97: mark#(U24(X1,X2,X3)) -> mark#(X1)
p98: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p99: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p100: mark#(U23(X1,X2,X3)) -> mark#(X1)
p101: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p102: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p103: mark#(U22(X1,X2,X3)) -> mark#(X1)
p104: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p105: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p106: mark#(U21(X1,X2,X3)) -> mark#(X1)
p107: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p108: active#(__(nil(),X)) -> mark#(X)
p109: mark#(isNeList(X)) -> active#(isNeList(X))
p110: active#(__(X,nil())) -> mark#(X)
p111: mark#(U13(X)) -> mark#(X)
p112: mark#(U13(X)) -> active#(U13(mark(X)))
p113: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p114: mark#(U12(X1,X2)) -> mark#(X1)
p115: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p116: mark#(U11(X1,X2)) -> mark#(X1)
p117: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p118: mark#(__(X1,X2)) -> mark#(X2)
p119: mark#(__(X1,X2)) -> mark#(X1)
p120: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = ((0,0),(1,0)) x1
      ___A(x1,x2) = (2,0)
      mark#_A(x1) = (0,2)
      U92_A(x1) = (1,1)
      mark_A(x1) = (1,1)
      isPalListKind_A(x1) = (2,0)
      U91_A(x1,x2) = (2,1)
      isPal_A(x1) = (2,0)
      U81_A(x1,x2) = (2,1)
      isNePal_A(x1) = (2,0)
      U71_A(x1,x2,x3) = (2,0)
      isQid_A(x1) = (1,0)
      U83_A(x1) = (2,0)
      U61_A(x1,x2) = (2,1)
      U82_A(x1,x2) = (2,0)
      isNeList_A(x1) = (2,0)
      U51_A(x1,x2,x3) = (2,0)
      U41_A(x1,x2,x3) = (2,0)
      U74_A(x1) = (2,0)
      U31_A(x1,x2) = (2,0)
      isList_A(x1) = (2,0)
      U21_A(x1,x2,x3) = (2,0)
      U73_A(x1,x2) = (2,1)
      U11_A(x1,x2) = (2,0)
      U72_A(x1,x2) = (2,1)
      tt_A() = (1,1)
      U63_A(x1) = (2,0)
      U62_A(x1,x2) = (2,1)
      U56_A(x1) = (2,1)
      U55_A(x1,x2) = (2,0)
      U54_A(x1,x2,x3) = (2,1)
      U53_A(x1,x2,x3) = (2,0)
      U52_A(x1,x2,x3) = (2,0)
      U46_A(x1) = (2,1)
      U45_A(x1,x2) = (2,1)
      U44_A(x1,x2,x3) = (2,0)
      U43_A(x1,x2,x3) = (2,0)
      U42_A(x1,x2,x3) = (2,0)
      U33_A(x1) = (1,0)
      U32_A(x1,x2) = (2,0)
      U25_A(x1,x2) = (2,0)
      U26_A(x1) = (2,0)
      U24_A(x1,x2,x3) = (2,0)
      U23_A(x1,x2,x3) = (2,0)
      U22_A(x1,x2,x3) = (2,0)
      U12_A(x1,x2) = (2,0)
      U13_A(x1) = (1,0)
      nil_A() = (1,0)
      active_A(x1) = (1,1)
      a_A() = (1,0)
      e_A() = (1,0)
      i_A() = (1,0)
      o_A() = (1,0)
      u_A() = (1,0)

The next rules are strictly ordered:

  p3, p78, p81, p112

We remove them from the problem.

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p4: mark#(U91(X1,X2)) -> mark#(X1)
p5: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p6: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p7: mark#(isNePal(X)) -> active#(isNePal(X))
p8: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p9: mark#(U83(X)) -> mark#(X)
p10: mark#(U83(X)) -> active#(U83(mark(X)))
p11: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p12: mark#(U82(X1,X2)) -> mark#(X1)
p13: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p14: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p15: mark#(U81(X1,X2)) -> mark#(X1)
p16: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p17: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p18: mark#(U74(X)) -> mark#(X)
p19: mark#(U74(X)) -> active#(U74(mark(X)))
p20: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p21: mark#(isPal(X)) -> active#(isPal(X))
p22: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p23: mark#(U73(X1,X2)) -> mark#(X1)
p24: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p25: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p26: mark#(U72(X1,X2)) -> mark#(X1)
p27: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p28: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p29: mark#(U71(X1,X2,X3)) -> mark#(X1)
p30: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p31: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p32: mark#(U63(X)) -> mark#(X)
p33: mark#(U63(X)) -> active#(U63(mark(X)))
p34: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p35: mark#(U62(X1,X2)) -> mark#(X1)
p36: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p37: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p38: mark#(U61(X1,X2)) -> mark#(X1)
p39: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p40: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p41: mark#(U56(X)) -> mark#(X)
p42: mark#(U56(X)) -> active#(U56(mark(X)))
p43: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p44: mark#(U55(X1,X2)) -> mark#(X1)
p45: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p46: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p47: mark#(U54(X1,X2,X3)) -> mark#(X1)
p48: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p49: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p50: mark#(U53(X1,X2,X3)) -> mark#(X1)
p51: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p52: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p53: mark#(U52(X1,X2,X3)) -> mark#(X1)
p54: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p55: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p56: mark#(U51(X1,X2,X3)) -> mark#(X1)
p57: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p58: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p59: mark#(U46(X)) -> mark#(X)
p60: mark#(U46(X)) -> active#(U46(mark(X)))
p61: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p62: mark#(U45(X1,X2)) -> mark#(X1)
p63: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p64: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p65: mark#(U44(X1,X2,X3)) -> mark#(X1)
p66: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p67: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p68: mark#(U43(X1,X2,X3)) -> mark#(X1)
p69: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p70: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p71: mark#(U42(X1,X2,X3)) -> mark#(X1)
p72: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p73: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p74: mark#(U41(X1,X2,X3)) -> mark#(X1)
p75: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p76: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p77: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p78: mark#(U33(X)) -> mark#(X)
p79: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p80: mark#(U32(X1,X2)) -> mark#(X1)
p81: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p82: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p83: mark#(U31(X1,X2)) -> mark#(X1)
p84: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p85: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p86: mark#(U26(X)) -> mark#(X)
p87: mark#(U26(X)) -> active#(U26(mark(X)))
p88: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p89: mark#(isList(X)) -> active#(isList(X))
p90: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p91: mark#(U25(X1,X2)) -> mark#(X1)
p92: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p93: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p94: mark#(U24(X1,X2,X3)) -> mark#(X1)
p95: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p96: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p97: mark#(U23(X1,X2,X3)) -> mark#(X1)
p98: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p99: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p100: mark#(U22(X1,X2,X3)) -> mark#(X1)
p101: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p102: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p103: mark#(U21(X1,X2,X3)) -> mark#(X1)
p104: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p105: active#(__(nil(),X)) -> mark#(X)
p106: mark#(isNeList(X)) -> active#(isNeList(X))
p107: active#(__(X,nil())) -> mark#(X)
p108: mark#(U13(X)) -> mark#(X)
p109: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p110: mark#(U12(X1,X2)) -> mark#(X1)
p111: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p112: mark#(U11(X1,X2)) -> mark#(X1)
p113: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p114: mark#(__(X1,X2)) -> mark#(X2)
p115: mark#(__(X1,X2)) -> mark#(X1)
p116: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {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, p85, p86, p87, p88, p89, p90, p91, p92, p93, p94, p95, p96, p97, p98, p99, p100, p101, p102, p103, p104, p105, p106, p107, p108, p109, p110, p111, p112, p113, p114, p115, p116}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p3: active#(__(X,nil())) -> mark#(X)
p4: mark#(__(X1,X2)) -> mark#(X1)
p5: mark#(__(X1,X2)) -> mark#(X2)
p6: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p7: active#(__(nil(),X)) -> mark#(X)
p8: mark#(U11(X1,X2)) -> mark#(X1)
p9: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p10: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p11: mark#(U12(X1,X2)) -> mark#(X1)
p12: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p13: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p14: mark#(U13(X)) -> mark#(X)
p15: mark#(isNeList(X)) -> active#(isNeList(X))
p16: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p17: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p18: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p19: mark#(U21(X1,X2,X3)) -> mark#(X1)
p20: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p21: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p22: mark#(U22(X1,X2,X3)) -> mark#(X1)
p23: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p24: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p25: mark#(U23(X1,X2,X3)) -> mark#(X1)
p26: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p27: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p28: mark#(U24(X1,X2,X3)) -> mark#(X1)
p29: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p30: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p31: mark#(U25(X1,X2)) -> mark#(X1)
p32: mark#(isList(X)) -> active#(isList(X))
p33: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p34: mark#(U26(X)) -> active#(U26(mark(X)))
p35: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p36: mark#(U26(X)) -> mark#(X)
p37: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p38: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p39: mark#(U31(X1,X2)) -> mark#(X1)
p40: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p41: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p42: mark#(U32(X1,X2)) -> mark#(X1)
p43: mark#(U33(X)) -> mark#(X)
p44: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p45: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p46: mark#(U41(X1,X2,X3)) -> mark#(X1)
p47: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p48: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p49: mark#(U42(X1,X2,X3)) -> mark#(X1)
p50: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p51: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p52: mark#(U43(X1,X2,X3)) -> mark#(X1)
p53: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p54: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p55: mark#(U44(X1,X2,X3)) -> mark#(X1)
p56: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p57: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p58: mark#(U45(X1,X2)) -> mark#(X1)
p59: mark#(U46(X)) -> active#(U46(mark(X)))
p60: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p61: mark#(U46(X)) -> mark#(X)
p62: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p63: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p64: mark#(U51(X1,X2,X3)) -> mark#(X1)
p65: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p66: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p67: mark#(U52(X1,X2,X3)) -> mark#(X1)
p68: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p69: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p70: mark#(U53(X1,X2,X3)) -> mark#(X1)
p71: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p72: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p73: mark#(U54(X1,X2,X3)) -> mark#(X1)
p74: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p75: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p76: mark#(U55(X1,X2)) -> mark#(X1)
p77: mark#(U56(X)) -> active#(U56(mark(X)))
p78: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p79: mark#(U56(X)) -> mark#(X)
p80: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p81: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p82: mark#(U61(X1,X2)) -> mark#(X1)
p83: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p84: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p85: mark#(U62(X1,X2)) -> mark#(X1)
p86: mark#(U63(X)) -> active#(U63(mark(X)))
p87: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p88: mark#(U63(X)) -> mark#(X)
p89: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p90: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p91: mark#(U71(X1,X2,X3)) -> mark#(X1)
p92: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p93: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p94: mark#(U72(X1,X2)) -> mark#(X1)
p95: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p96: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p97: mark#(U73(X1,X2)) -> mark#(X1)
p98: mark#(isPal(X)) -> active#(isPal(X))
p99: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p100: mark#(U74(X)) -> active#(U74(mark(X)))
p101: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p102: mark#(U74(X)) -> mark#(X)
p103: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p104: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p105: mark#(U81(X1,X2)) -> mark#(X1)
p106: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p107: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p108: mark#(U82(X1,X2)) -> mark#(X1)
p109: mark#(U83(X)) -> active#(U83(mark(X)))
p110: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p111: mark#(U83(X)) -> mark#(X)
p112: mark#(isNePal(X)) -> active#(isNePal(X))
p113: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p114: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p115: mark#(U91(X1,X2)) -> mark#(X1)
p116: mark#(U92(X)) -> mark#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = ((0,0),(1,0)) x1
      ___A(x1,x2) = (2,1)
      mark#_A(x1) = (0,2)
      mark_A(x1) = (1,1)
      nil_A() = (0,0)
      U11_A(x1,x2) = (2,1)
      U12_A(x1,x2) = (2,0)
      tt_A() = (1,0)
      isPalListKind_A(x1) = (2,1)
      U13_A(x1) = (1,1)
      isNeList_A(x1) = (2,1)
      U21_A(x1,x2,x3) = (2,0)
      U22_A(x1,x2,x3) = (2,0)
      U23_A(x1,x2,x3) = (2,0)
      U24_A(x1,x2,x3) = (2,1)
      U25_A(x1,x2) = (2,1)
      isList_A(x1) = (2,1)
      U26_A(x1) = (1,1)
      U31_A(x1,x2) = (2,1)
      U32_A(x1,x2) = (2,1)
      U33_A(x1) = (1,1)
      isQid_A(x1) = (1,1)
      U41_A(x1,x2,x3) = (2,1)
      U42_A(x1,x2,x3) = (2,0)
      U43_A(x1,x2,x3) = (2,0)
      U44_A(x1,x2,x3) = (2,0)
      U45_A(x1,x2) = (2,1)
      U46_A(x1) = (2,0)
      U51_A(x1,x2,x3) = (2,1)
      U52_A(x1,x2,x3) = (2,1)
      U53_A(x1,x2,x3) = (2,0)
      U54_A(x1,x2,x3) = (2,0)
      U55_A(x1,x2) = (2,0)
      U56_A(x1) = (2,0)
      U61_A(x1,x2) = (2,0)
      U62_A(x1,x2) = (2,0)
      U63_A(x1) = (2,0)
      U71_A(x1,x2,x3) = (2,0)
      U72_A(x1,x2) = (2,0)
      U73_A(x1,x2) = (2,1)
      isPal_A(x1) = (2,1)
      U74_A(x1) = (2,1)
      U81_A(x1,x2) = (2,0)
      U82_A(x1,x2) = (2,1)
      U83_A(x1) = (2,1)
      isNePal_A(x1) = (2,0)
      U91_A(x1,x2) = (2,1)
      U92_A(x1) = (1,1)
      active_A(x1) = (1,1)
      a_A() = (1,0)
      e_A() = (1,0)
      i_A() = (1,0)
      o_A() = (1,0)
      u_A() = (1,0)

The next rules are strictly ordered:

  p34

We remove them from the problem.

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p3: active#(__(X,nil())) -> mark#(X)
p4: mark#(__(X1,X2)) -> mark#(X1)
p5: mark#(__(X1,X2)) -> mark#(X2)
p6: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p7: active#(__(nil(),X)) -> mark#(X)
p8: mark#(U11(X1,X2)) -> mark#(X1)
p9: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p10: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p11: mark#(U12(X1,X2)) -> mark#(X1)
p12: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p13: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p14: mark#(U13(X)) -> mark#(X)
p15: mark#(isNeList(X)) -> active#(isNeList(X))
p16: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p17: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p18: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p19: mark#(U21(X1,X2,X3)) -> mark#(X1)
p20: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p21: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p22: mark#(U22(X1,X2,X3)) -> mark#(X1)
p23: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p24: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p25: mark#(U23(X1,X2,X3)) -> mark#(X1)
p26: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p27: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p28: mark#(U24(X1,X2,X3)) -> mark#(X1)
p29: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p30: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p31: mark#(U25(X1,X2)) -> mark#(X1)
p32: mark#(isList(X)) -> active#(isList(X))
p33: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p34: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p35: mark#(U26(X)) -> mark#(X)
p36: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p37: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p38: mark#(U31(X1,X2)) -> mark#(X1)
p39: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p40: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p41: mark#(U32(X1,X2)) -> mark#(X1)
p42: mark#(U33(X)) -> mark#(X)
p43: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p44: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p45: mark#(U41(X1,X2,X3)) -> mark#(X1)
p46: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p47: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p48: mark#(U42(X1,X2,X3)) -> mark#(X1)
p49: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p50: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p51: mark#(U43(X1,X2,X3)) -> mark#(X1)
p52: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p53: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p54: mark#(U44(X1,X2,X3)) -> mark#(X1)
p55: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p56: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p57: mark#(U45(X1,X2)) -> mark#(X1)
p58: mark#(U46(X)) -> active#(U46(mark(X)))
p59: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p60: mark#(U46(X)) -> mark#(X)
p61: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p62: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p63: mark#(U51(X1,X2,X3)) -> mark#(X1)
p64: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p65: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p66: mark#(U52(X1,X2,X3)) -> mark#(X1)
p67: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p68: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p69: mark#(U53(X1,X2,X3)) -> mark#(X1)
p70: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p71: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p72: mark#(U54(X1,X2,X3)) -> mark#(X1)
p73: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p74: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p75: mark#(U55(X1,X2)) -> mark#(X1)
p76: mark#(U56(X)) -> active#(U56(mark(X)))
p77: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p78: mark#(U56(X)) -> mark#(X)
p79: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p80: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p81: mark#(U61(X1,X2)) -> mark#(X1)
p82: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p83: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p84: mark#(U62(X1,X2)) -> mark#(X1)
p85: mark#(U63(X)) -> active#(U63(mark(X)))
p86: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p87: mark#(U63(X)) -> mark#(X)
p88: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p89: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p90: mark#(U71(X1,X2,X3)) -> mark#(X1)
p91: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p92: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p93: mark#(U72(X1,X2)) -> mark#(X1)
p94: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p95: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p96: mark#(U73(X1,X2)) -> mark#(X1)
p97: mark#(isPal(X)) -> active#(isPal(X))
p98: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p99: mark#(U74(X)) -> active#(U74(mark(X)))
p100: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p101: mark#(U74(X)) -> mark#(X)
p102: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p103: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p104: mark#(U81(X1,X2)) -> mark#(X1)
p105: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p106: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p107: mark#(U82(X1,X2)) -> mark#(X1)
p108: mark#(U83(X)) -> active#(U83(mark(X)))
p109: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p110: mark#(U83(X)) -> mark#(X)
p111: mark#(isNePal(X)) -> active#(isNePal(X))
p112: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p113: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p114: mark#(U91(X1,X2)) -> mark#(X1)
p115: mark#(U92(X)) -> mark#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {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, p85, p86, p87, p88, p89, p90, p91, p92, p93, p94, p95, p96, p97, p98, p99, p100, p101, p102, p103, p104, p105, p106, p107, p108, p109, p110, p111, p112, p113, p114, p115}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: mark#(U91(X1,X2)) -> mark#(X1)
p4: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p5: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p6: mark#(isNePal(X)) -> active#(isNePal(X))
p7: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p8: mark#(U83(X)) -> mark#(X)
p9: mark#(U83(X)) -> active#(U83(mark(X)))
p10: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p11: mark#(U82(X1,X2)) -> mark#(X1)
p12: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p13: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p14: mark#(U81(X1,X2)) -> mark#(X1)
p15: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p16: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p17: mark#(U74(X)) -> mark#(X)
p18: mark#(U74(X)) -> active#(U74(mark(X)))
p19: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p20: mark#(isPal(X)) -> active#(isPal(X))
p21: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p22: mark#(U73(X1,X2)) -> mark#(X1)
p23: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p24: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p25: mark#(U72(X1,X2)) -> mark#(X1)
p26: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p27: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p28: mark#(U71(X1,X2,X3)) -> mark#(X1)
p29: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p30: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p31: mark#(U63(X)) -> mark#(X)
p32: mark#(U63(X)) -> active#(U63(mark(X)))
p33: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p34: mark#(U62(X1,X2)) -> mark#(X1)
p35: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p36: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p37: mark#(U61(X1,X2)) -> mark#(X1)
p38: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p39: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p40: mark#(U56(X)) -> mark#(X)
p41: mark#(U56(X)) -> active#(U56(mark(X)))
p42: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p43: mark#(U55(X1,X2)) -> mark#(X1)
p44: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p45: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p46: mark#(U54(X1,X2,X3)) -> mark#(X1)
p47: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p48: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p49: mark#(U53(X1,X2,X3)) -> mark#(X1)
p50: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p51: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p52: mark#(U52(X1,X2,X3)) -> mark#(X1)
p53: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p54: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p55: mark#(U51(X1,X2,X3)) -> mark#(X1)
p56: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p57: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p58: mark#(U46(X)) -> mark#(X)
p59: mark#(U46(X)) -> active#(U46(mark(X)))
p60: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p61: mark#(U45(X1,X2)) -> mark#(X1)
p62: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p63: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p64: mark#(U44(X1,X2,X3)) -> mark#(X1)
p65: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p66: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p67: mark#(U43(X1,X2,X3)) -> mark#(X1)
p68: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p69: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p70: mark#(U42(X1,X2,X3)) -> mark#(X1)
p71: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p72: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p73: mark#(U41(X1,X2,X3)) -> mark#(X1)
p74: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p75: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p76: mark#(U33(X)) -> mark#(X)
p77: mark#(U32(X1,X2)) -> mark#(X1)
p78: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p79: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p80: mark#(U31(X1,X2)) -> mark#(X1)
p81: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p82: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p83: mark#(U26(X)) -> mark#(X)
p84: mark#(isList(X)) -> active#(isList(X))
p85: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p86: mark#(U25(X1,X2)) -> mark#(X1)
p87: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p88: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p89: mark#(U24(X1,X2,X3)) -> mark#(X1)
p90: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p91: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p92: mark#(U23(X1,X2,X3)) -> mark#(X1)
p93: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p94: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p95: mark#(U22(X1,X2,X3)) -> mark#(X1)
p96: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p97: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p98: mark#(U21(X1,X2,X3)) -> mark#(X1)
p99: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p100: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p101: mark#(isNeList(X)) -> active#(isNeList(X))
p102: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p103: mark#(U13(X)) -> mark#(X)
p104: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p105: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p106: mark#(U12(X1,X2)) -> mark#(X1)
p107: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p108: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p109: mark#(U11(X1,X2)) -> mark#(X1)
p110: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p111: active#(__(nil(),X)) -> mark#(X)
p112: mark#(__(X1,X2)) -> mark#(X2)
p113: mark#(__(X1,X2)) -> mark#(X1)
p114: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p115: active#(__(X,nil())) -> mark#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = ((0,0),(1,0)) x1
      ___A(x1,x2) = (2,1)
      mark#_A(x1) = (0,2)
      U92_A(x1) = (1,1)
      U91_A(x1,x2) = (2,1)
      mark_A(x1) = (1,1)
      isPalListKind_A(x1) = (2,1)
      isNePal_A(x1) = (2,1)
      isPal_A(x1) = (2,1)
      U81_A(x1,x2) = (2,1)
      U83_A(x1) = (1,1)
      U71_A(x1,x2,x3) = (2,0)
      isQid_A(x1) = (1,1)
      U82_A(x1,x2) = (2,1)
      U61_A(x1,x2) = (2,1)
      isNeList_A(x1) = (2,1)
      U51_A(x1,x2,x3) = (2,1)
      U74_A(x1) = (1,1)
      U41_A(x1,x2,x3) = (2,1)
      U31_A(x1,x2) = (2,1)
      U73_A(x1,x2) = (2,1)
      isList_A(x1) = (2,1)
      U21_A(x1,x2,x3) = (2,1)
      U72_A(x1,x2) = (2,1)
      U11_A(x1,x2) = (2,1)
      tt_A() = (1,1)
      U63_A(x1) = (1,1)
      U62_A(x1,x2) = (2,1)
      U56_A(x1) = (1,1)
      U55_A(x1,x2) = (2,1)
      U54_A(x1,x2,x3) = (2,1)
      U53_A(x1,x2,x3) = (2,1)
      U52_A(x1,x2,x3) = (2,1)
      U46_A(x1) = (1,1)
      U45_A(x1,x2) = (2,1)
      U44_A(x1,x2,x3) = (2,1)
      U43_A(x1,x2,x3) = (2,1)
      U42_A(x1,x2,x3) = (2,1)
      U33_A(x1) = (1,0)
      U32_A(x1,x2) = (2,1)
      U26_A(x1) = (1,1)
      U25_A(x1,x2) = (2,1)
      U24_A(x1,x2,x3) = (2,1)
      U23_A(x1,x2,x3) = (2,1)
      U22_A(x1,x2,x3) = (2,1)
      U13_A(x1) = (1,1)
      U12_A(x1,x2) = (2,1)
      nil_A() = (1,1)
      active_A(x1) = (1,1)
      a_A() = (1,1)
      e_A() = (1,1)
      i_A() = (1,1)
      o_A() = (1,1)
      u_A() = (1,1)

The next rules are strictly ordered:

  p9, p18, p32, p41, p59

We remove them from the problem.

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: mark#(U91(X1,X2)) -> mark#(X1)
p4: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p5: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p6: mark#(isNePal(X)) -> active#(isNePal(X))
p7: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p8: mark#(U83(X)) -> mark#(X)
p9: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p10: mark#(U82(X1,X2)) -> mark#(X1)
p11: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p12: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p13: mark#(U81(X1,X2)) -> mark#(X1)
p14: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p15: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p16: mark#(U74(X)) -> mark#(X)
p17: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p18: mark#(isPal(X)) -> active#(isPal(X))
p19: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p20: mark#(U73(X1,X2)) -> mark#(X1)
p21: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p22: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p23: mark#(U72(X1,X2)) -> mark#(X1)
p24: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p25: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p26: mark#(U71(X1,X2,X3)) -> mark#(X1)
p27: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p28: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p29: mark#(U63(X)) -> mark#(X)
p30: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p31: mark#(U62(X1,X2)) -> mark#(X1)
p32: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p33: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p34: mark#(U61(X1,X2)) -> mark#(X1)
p35: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p36: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p37: mark#(U56(X)) -> mark#(X)
p38: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p39: mark#(U55(X1,X2)) -> mark#(X1)
p40: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p41: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p42: mark#(U54(X1,X2,X3)) -> mark#(X1)
p43: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p44: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p45: mark#(U53(X1,X2,X3)) -> mark#(X1)
p46: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p47: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p48: mark#(U52(X1,X2,X3)) -> mark#(X1)
p49: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p50: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p51: mark#(U51(X1,X2,X3)) -> mark#(X1)
p52: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p53: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p54: mark#(U46(X)) -> mark#(X)
p55: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p56: mark#(U45(X1,X2)) -> mark#(X1)
p57: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p58: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p59: mark#(U44(X1,X2,X3)) -> mark#(X1)
p60: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p61: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p62: mark#(U43(X1,X2,X3)) -> mark#(X1)
p63: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p64: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p65: mark#(U42(X1,X2,X3)) -> mark#(X1)
p66: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p67: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p68: mark#(U41(X1,X2,X3)) -> mark#(X1)
p69: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p70: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p71: mark#(U33(X)) -> mark#(X)
p72: mark#(U32(X1,X2)) -> mark#(X1)
p73: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p74: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p75: mark#(U31(X1,X2)) -> mark#(X1)
p76: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p77: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p78: mark#(U26(X)) -> mark#(X)
p79: mark#(isList(X)) -> active#(isList(X))
p80: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p81: mark#(U25(X1,X2)) -> mark#(X1)
p82: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p83: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p84: mark#(U24(X1,X2,X3)) -> mark#(X1)
p85: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p86: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p87: mark#(U23(X1,X2,X3)) -> mark#(X1)
p88: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p89: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p90: mark#(U22(X1,X2,X3)) -> mark#(X1)
p91: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p92: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p93: mark#(U21(X1,X2,X3)) -> mark#(X1)
p94: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p95: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p96: mark#(isNeList(X)) -> active#(isNeList(X))
p97: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p98: mark#(U13(X)) -> mark#(X)
p99: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p100: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p101: mark#(U12(X1,X2)) -> mark#(X1)
p102: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p103: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p104: mark#(U11(X1,X2)) -> mark#(X1)
p105: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p106: active#(__(nil(),X)) -> mark#(X)
p107: mark#(__(X1,X2)) -> mark#(X2)
p108: mark#(__(X1,X2)) -> mark#(X1)
p109: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p110: active#(__(X,nil())) -> mark#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {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, p85, p86, p87, p88, p89, p90, p91, p92, p93, p94, p95, p96, p97, p98, p99, p100, p101, p102, p103, p104, p105, p106, p107, p108, p109, p110}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p3: active#(__(X,nil())) -> mark#(X)
p4: mark#(__(X1,X2)) -> mark#(X1)
p5: mark#(__(X1,X2)) -> mark#(X2)
p6: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p7: active#(__(nil(),X)) -> mark#(X)
p8: mark#(U11(X1,X2)) -> mark#(X1)
p9: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p10: active#(U11(tt(),V)) -> mark#(U12(isPalListKind(V),V))
p11: mark#(U12(X1,X2)) -> mark#(X1)
p12: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p13: active#(U12(tt(),V)) -> mark#(U13(isNeList(V)))
p14: mark#(U13(X)) -> mark#(X)
p15: mark#(isNeList(X)) -> active#(isNeList(X))
p16: active#(U21(tt(),V1,V2)) -> mark#(U22(isPalListKind(V1),V1,V2))
p17: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p18: active#(U22(tt(),V1,V2)) -> mark#(U23(isPalListKind(V2),V1,V2))
p19: mark#(U21(X1,X2,X3)) -> mark#(X1)
p20: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p21: active#(U23(tt(),V1,V2)) -> mark#(U24(isPalListKind(V2),V1,V2))
p22: mark#(U22(X1,X2,X3)) -> mark#(X1)
p23: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p24: active#(U24(tt(),V1,V2)) -> mark#(U25(isList(V1),V2))
p25: mark#(U23(X1,X2,X3)) -> mark#(X1)
p26: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p27: active#(U25(tt(),V2)) -> mark#(U26(isList(V2)))
p28: mark#(U24(X1,X2,X3)) -> mark#(X1)
p29: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p30: active#(U31(tt(),V)) -> mark#(U32(isPalListKind(V),V))
p31: mark#(U25(X1,X2)) -> mark#(X1)
p32: mark#(isList(X)) -> active#(isList(X))
p33: active#(U32(tt(),V)) -> mark#(U33(isQid(V)))
p34: mark#(U26(X)) -> mark#(X)
p35: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p36: active#(U41(tt(),V1,V2)) -> mark#(U42(isPalListKind(V1),V1,V2))
p37: mark#(U31(X1,X2)) -> mark#(X1)
p38: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p39: active#(U42(tt(),V1,V2)) -> mark#(U43(isPalListKind(V2),V1,V2))
p40: mark#(U32(X1,X2)) -> mark#(X1)
p41: mark#(U33(X)) -> mark#(X)
p42: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p43: active#(U43(tt(),V1,V2)) -> mark#(U44(isPalListKind(V2),V1,V2))
p44: mark#(U41(X1,X2,X3)) -> mark#(X1)
p45: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p46: active#(U44(tt(),V1,V2)) -> mark#(U45(isList(V1),V2))
p47: mark#(U42(X1,X2,X3)) -> mark#(X1)
p48: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p49: active#(U45(tt(),V2)) -> mark#(U46(isNeList(V2)))
p50: mark#(U43(X1,X2,X3)) -> mark#(X1)
p51: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p52: active#(U51(tt(),V1,V2)) -> mark#(U52(isPalListKind(V1),V1,V2))
p53: mark#(U44(X1,X2,X3)) -> mark#(X1)
p54: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p55: active#(U52(tt(),V1,V2)) -> mark#(U53(isPalListKind(V2),V1,V2))
p56: mark#(U45(X1,X2)) -> mark#(X1)
p57: mark#(U46(X)) -> mark#(X)
p58: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p59: active#(U53(tt(),V1,V2)) -> mark#(U54(isPalListKind(V2),V1,V2))
p60: mark#(U51(X1,X2,X3)) -> mark#(X1)
p61: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p62: active#(U54(tt(),V1,V2)) -> mark#(U55(isNeList(V1),V2))
p63: mark#(U52(X1,X2,X3)) -> mark#(X1)
p64: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p65: active#(U55(tt(),V2)) -> mark#(U56(isList(V2)))
p66: mark#(U53(X1,X2,X3)) -> mark#(X1)
p67: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p68: active#(U61(tt(),V)) -> mark#(U62(isPalListKind(V),V))
p69: mark#(U54(X1,X2,X3)) -> mark#(X1)
p70: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p71: active#(U62(tt(),V)) -> mark#(U63(isQid(V)))
p72: mark#(U55(X1,X2)) -> mark#(X1)
p73: mark#(U56(X)) -> mark#(X)
p74: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p75: active#(U71(tt(),I,P)) -> mark#(U72(isPalListKind(I),P))
p76: mark#(U61(X1,X2)) -> mark#(X1)
p77: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p78: active#(U72(tt(),P)) -> mark#(U73(isPal(P),P))
p79: mark#(U62(X1,X2)) -> mark#(X1)
p80: mark#(U63(X)) -> mark#(X)
p81: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p82: active#(U73(tt(),P)) -> mark#(U74(isPalListKind(P)))
p83: mark#(U71(X1,X2,X3)) -> mark#(X1)
p84: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p85: active#(U81(tt(),V)) -> mark#(U82(isPalListKind(V),V))
p86: mark#(U72(X1,X2)) -> mark#(X1)
p87: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p88: active#(U82(tt(),V)) -> mark#(U83(isNePal(V)))
p89: mark#(U73(X1,X2)) -> mark#(X1)
p90: mark#(isPal(X)) -> active#(isPal(X))
p91: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p92: mark#(U74(X)) -> mark#(X)
p93: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p94: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p95: mark#(U81(X1,X2)) -> mark#(X1)
p96: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p97: active#(isList(__(V1,V2))) -> mark#(U21(isPalListKind(V1),V1,V2))
p98: mark#(U82(X1,X2)) -> mark#(X1)
p99: mark#(U83(X)) -> mark#(X)
p100: mark#(isNePal(X)) -> active#(isNePal(X))
p101: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p102: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p103: active#(isNeList(__(V1,V2))) -> mark#(U41(isPalListKind(V1),V1,V2))
p104: mark#(U91(X1,X2)) -> mark#(X1)
p105: mark#(U92(X)) -> mark#(X)
p106: active#(isNeList(__(V1,V2))) -> mark#(U51(isPalListKind(V1),V1,V2))
p107: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p108: active#(isNePal(__(I,__(P,I)))) -> mark#(U71(isQid(I),I,P))
p109: active#(isPal(V)) -> mark#(U81(isPalListKind(V),V))
p110: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))

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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = ((0,0),(1,0)) x1
      ___A(x1,x2) = x1 + ((1,0),(1,0)) x2 + (15,1)
      mark#_A(x1) = ((0,0),(1,0)) x1
      mark_A(x1) = x1 + (0,1)
      nil_A() = (1,1)
      U11_A(x1,x2) = x1 + x2 + (7,1)
      U12_A(x1,x2) = x1 + x2 + (6,1)
      tt_A() = (1,1)
      isPalListKind_A(x1) = ((0,0),(1,0)) x1 + (1,1)
      U13_A(x1) = x1 + (1,1)
      isNeList_A(x1) = ((1,0),(1,0)) x1 + (5,1)
      U21_A(x1,x2,x3) = x1 + x2 + x3 + (22,1)
      U22_A(x1,x2,x3) = x1 + x2 + x3 + (21,1)
      U23_A(x1,x2,x3) = x1 + x2 + x3 + (20,1)
      U24_A(x1,x2,x3) = x1 + x2 + x3 + (19,1)
      U25_A(x1,x2) = x1 + x2 + (10,1)
      isList_A(x1) = ((1,0),(1,0)) x1 + (9,1)
      U26_A(x1) = ((1,0),(1,0)) x1 + (1,1)
      U31_A(x1,x2) = ((1,0),(1,0)) x1 + (3,1)
      U32_A(x1,x2) = x1 + (2,1)
      U33_A(x1) = x1 + (1,1)
      isQid_A(x1) = (1,1)
      U41_A(x1,x2,x3) = ((1,0),(1,0)) x1 + x2 + x3 + (18,1)
      U42_A(x1,x2,x3) = ((1,0),(1,0)) x1 + x2 + x3 + (17,1)
      U43_A(x1,x2,x3) = ((1,0),(1,0)) x1 + x2 + x3 + (16,1)
      U44_A(x1,x2,x3) = ((1,0),(1,0)) x1 + x2 + x3 + (15,1)
      U45_A(x1,x2) = x1 + x2 + (6,1)
      U46_A(x1) = x1 + (1,1)
      U51_A(x1,x2,x3) = x1 + ((1,0),(1,0)) x2 + x3 + (18,1)
      U52_A(x1,x2,x3) = ((1,0),(1,0)) x1 + x2 + x3 + (17,1)
      U53_A(x1,x2,x3) = x1 + x2 + x3 + (16,1)
      U54_A(x1,x2,x3) = x1 + x2 + ((1,0),(1,0)) x3 + (15,1)
      U55_A(x1,x2) = ((1,0),(1,0)) x1 + x2 + (10,1)
      U56_A(x1) = x1 + (1,1)
      U61_A(x1,x2) = x1 + x2 + (3,1)
      U62_A(x1,x2) = x1 + x2 + (2,1)
      U63_A(x1) = x1 + (1,1)
      U71_A(x1,x2,x3) = ((1,0),(1,0)) x1 + x3 + (12,1)
      U72_A(x1,x2) = ((1,0),(1,0)) x1 + x2 + (11,1)
      U73_A(x1,x2) = ((1,0),(1,0)) x1 + (2,1)
      isPal_A(x1) = x1 + (9,1)
      U74_A(x1) = x1 + (1,1)
      U81_A(x1,x2) = x1 + x2 + (7,1)
      U82_A(x1,x2) = x1 + x2 + (6,1)
      U83_A(x1) = x1 + (1,1)
      isNePal_A(x1) = ((1,0),(1,0)) x1 + (5,1)
      U91_A(x1,x2) = x1 + (0,1)
      U92_A(x1) = x1 + (0,1)
      active_A(x1) = x1 + (0,1)
      a_A() = (0,1)
      e_A() = (0,1)
      i_A() = (0,1)
      o_A() = (0,1)
      u_A() = (1,1)

The next rules are strictly ordered:

  p3, p4, p5, p7, p8, p10, p11, p13, p14, p16, p18, p19, p21, p22, p24, p25, p27, p28, p30, p31, p33, p34, p36, p37, p39, p40, p41, p43, p44, p46, p47, p49, p50, p52, p53, p55, p56, p57, p59, p60, p62, p63, p65, p66, p68, p69, p71, p72, p73, p75, p76, p78, p79, p80, p82, p83, p85, p86, p88, p89, p92, p94, p95, p97, p98, p99, p101, p103, p106, p107, p108, p109

We remove them from the problem.

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p3: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p4: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p5: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p6: mark#(isNeList(X)) -> active#(isNeList(X))
p7: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p8: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p9: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p10: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p11: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p12: mark#(isList(X)) -> active#(isList(X))
p13: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p14: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p15: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p16: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p17: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p18: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p19: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p20: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p21: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p22: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p23: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p24: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p25: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p26: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p27: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p28: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p29: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p30: mark#(isPal(X)) -> active#(isPal(X))
p31: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p32: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p33: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p34: mark#(isNePal(X)) -> active#(isNePal(X))
p35: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p36: mark#(U91(X1,X2)) -> mark#(X1)
p37: mark#(U92(X)) -> mark#(X)
p38: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))

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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {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}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: mark#(U91(X1,X2)) -> mark#(X1)
p4: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p5: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p6: mark#(isNePal(X)) -> active#(isNePal(X))
p7: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p8: mark#(U82(X1,X2)) -> active#(U82(mark(X1),X2))
p9: mark#(U81(X1,X2)) -> active#(U81(mark(X1),X2))
p10: mark#(isPal(X)) -> active#(isPal(X))
p11: mark#(U73(X1,X2)) -> active#(U73(mark(X1),X2))
p12: mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2))
p13: mark#(U71(X1,X2,X3)) -> active#(U71(mark(X1),X2,X3))
p14: mark#(U62(X1,X2)) -> active#(U62(mark(X1),X2))
p15: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p16: mark#(U55(X1,X2)) -> active#(U55(mark(X1),X2))
p17: mark#(U54(X1,X2,X3)) -> active#(U54(mark(X1),X2,X3))
p18: mark#(U53(X1,X2,X3)) -> active#(U53(mark(X1),X2,X3))
p19: mark#(U52(X1,X2,X3)) -> active#(U52(mark(X1),X2,X3))
p20: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p21: mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2))
p22: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p23: mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3))
p24: mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3))
p25: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p26: mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2))
p27: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p28: mark#(isList(X)) -> active#(isList(X))
p29: mark#(U25(X1,X2)) -> active#(U25(mark(X1),X2))
p30: mark#(U24(X1,X2,X3)) -> active#(U24(mark(X1),X2,X3))
p31: mark#(U23(X1,X2,X3)) -> active#(U23(mark(X1),X2,X3))
p32: mark#(U22(X1,X2,X3)) -> active#(U22(mark(X1),X2,X3))
p33: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p34: mark#(isNeList(X)) -> active#(isNeList(X))
p35: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p36: mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2))
p37: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p38: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = ((0,0),(1,0)) x1
      ___A(x1,x2) = (2,0)
      mark#_A(x1) = (0,2)
      U92_A(x1) = (1,1)
      U91_A(x1,x2) = (2,1)
      mark_A(x1) = (1,1)
      isPalListKind_A(x1) = (2,1)
      isNePal_A(x1) = (1,0)
      tt_A() = (1,1)
      U82_A(x1,x2) = (1,1)
      U81_A(x1,x2) = (1,0)
      isPal_A(x1) = (1,1)
      U73_A(x1,x2) = (1,0)
      U72_A(x1,x2) = (1,0)
      U71_A(x1,x2,x3) = (1,1)
      U62_A(x1,x2) = (1,0)
      U61_A(x1,x2) = (1,0)
      U55_A(x1,x2) = (1,0)
      U54_A(x1,x2,x3) = (1,0)
      U53_A(x1,x2,x3) = (1,1)
      U52_A(x1,x2,x3) = (1,0)
      U51_A(x1,x2,x3) = (1,1)
      U45_A(x1,x2) = (1,0)
      U44_A(x1,x2,x3) = (2,0)
      U43_A(x1,x2,x3) = (1,0)
      U42_A(x1,x2,x3) = (1,0)
      U41_A(x1,x2,x3) = (1,0)
      U32_A(x1,x2) = (1,0)
      U31_A(x1,x2) = (1,0)
      isList_A(x1) = (1,1)
      U25_A(x1,x2) = (1,1)
      U24_A(x1,x2,x3) = (1,0)
      U23_A(x1,x2,x3) = (1,0)
      U22_A(x1,x2,x3) = (1,0)
      U21_A(x1,x2,x3) = (1,0)
      isNeList_A(x1) = (1,1)
      U12_A(x1,x2) = (0,0)
      U11_A(x1,x2) = (1,0)
      active_A(x1) = (1,1)
      nil_A() = (1,0)
      U13_A(x1) = (1,0)
      U26_A(x1) = (1,0)
      U33_A(x1) = (1,0)
      isQid_A(x1) = (1,0)
      U46_A(x1) = (1,0)
      U56_A(x1) = (1,0)
      U63_A(x1) = (1,1)
      U74_A(x1) = (1,0)
      U83_A(x1) = (1,0)
      a_A() = (1,0)
      e_A() = (1,0)
      i_A() = (1,0)
      o_A() = (1,0)
      u_A() = (1,0)

The next rules are strictly ordered:

  p6, p8, p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, p23, p24, p25, p26, p27, p28, p29, p30, p31, p32, p33, p34, p36, p37

We remove them from the problem.

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: mark#(U91(X1,X2)) -> mark#(X1)
p4: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p5: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p6: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p7: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p8: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p9: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4, p5, p6, p7, p8, p9}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p3: active#(U91(tt(),V2)) -> mark#(U92(isPalListKind(V2)))
p4: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p5: active#(isPalListKind(__(V1,V2))) -> mark#(U91(isPalListKind(V1),V2))
p6: mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3))
p7: mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2))
p8: mark#(U91(X1,X2)) -> mark#(X1)
p9: mark#(U92(X)) -> mark#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = x1
      ___A(x1,x2) = x1 + x2 + (3,2)
      mark#_A(x1) = x1 + (0,2)
      mark_A(x1) = x1 + (0,1)
      U91_A(x1,x2) = x1 + x2 + (2,1)
      tt_A() = (0,1)
      U92_A(x1) = ((1,0),(1,0)) x1 + (0,1)
      isPalListKind_A(x1) = x1 + (1,1)
      U44_A(x1,x2,x3) = x1 + x2 + (5,1)
      active_A(x1) = x1 + (0,1)
      nil_A() = (1,1)
      U11_A(x1,x2) = ((1,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (1,1)
      U12_A(x1,x2) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (1,1)
      U13_A(x1) = ((0,0),(1,0)) x1 + (0,1)
      isNeList_A(x1) = ((1,0),(1,0)) x1 + (3,1)
      U21_A(x1,x2,x3) = x1 + ((0,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (1,1)
      U22_A(x1,x2,x3) = ((0,0),(1,0)) x2 + x3 + (1,1)
      U23_A(x1,x2,x3) = ((0,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (1,1)
      U24_A(x1,x2,x3) = ((1,0),(1,0)) x1 + ((0,0),(1,0)) x2 + ((0,0),(1,0)) x3 + (0,1)
      U25_A(x1,x2) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (0,1)
      isList_A(x1) = x1 + (3,1)
      U26_A(x1) = ((0,0),(1,0)) x1 + (0,1)
      U31_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + (3,1)
      U32_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + (2,1)
      U33_A(x1) = ((1,0),(1,0)) x1 + (1,1)
      isQid_A(x1) = x1 + (0,1)
      U41_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (6,1)
      U42_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (6,1)
      U43_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (6,1)
      U45_A(x1,x2) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (0,1)
      U46_A(x1) = ((0,0),(1,0)) x1 + (0,1)
      U51_A(x1,x2,x3) = ((1,0),(1,0)) x1 + ((1,0),(1,0)) x3 + (5,1)
      U52_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (5,1)
      U53_A(x1,x2,x3) = ((1,0),(1,0)) x3 + (5,1)
      U54_A(x1,x2,x3) = x1 + ((0,0),(1,0)) x2 + ((0,0),(1,0)) x3 + (0,1)
      U55_A(x1,x2) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (0,1)
      U56_A(x1) = ((0,0),(1,0)) x1 + (0,1)
      U61_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + (2,1)
      U62_A(x1,x2) = ((1,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (1,1)
      U63_A(x1) = ((0,0),(1,0)) x1 + (1,1)
      U71_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (0,1)
      U72_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + (0,1)
      U73_A(x1,x2) = ((0,0),(1,0)) x1 + x2 + (0,1)
      isPal_A(x1) = ((1,0),(1,0)) x1 + (2,1)
      U74_A(x1) = ((0,0),(1,0)) x1 + (0,1)
      U81_A(x1,x2) = x2 + (2,1)
      U82_A(x1,x2) = ((1,0),(1,0)) x2 + (2,1)
      U83_A(x1) = x1 + (0,1)
      isNePal_A(x1) = ((1,0),(1,0)) x1 + (2,1)
      a_A() = (0,1)
      e_A() = (0,1)
      i_A() = (1,1)
      o_A() = (1,1)
      u_A() = (1,1)

The next rules are strictly ordered:

  p3, p4, p5, p6, p7, p8

We remove them from the problem.

-- SCC decomposition.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p3: mark#(U92(X)) -> mark#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(U92(X)) -> mark#(X)
p3: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = ((1,0),(1,1)) x1
      ___A(x1,x2) = x1 + x2 + (7,0)
      mark#_A(x1) = ((1,0),(1,0)) x1
      U92_A(x1) = x1 + (1,0)
      mark_A(x1) = x1 + (0,1)
      active_A(x1) = x1 + (0,1)
      nil_A() = (13,1)
      U11_A(x1,x2) = x2 + (8,1)
      tt_A() = (13,1)
      U12_A(x1,x2) = x2 + (7,1)
      isPalListKind_A(x1) = x1 + (1,1)
      U13_A(x1) = x1 + (1,1)
      isNeList_A(x1) = x1 + (5,1)
      U21_A(x1,x2,x3) = x2 + x3 + (3,1)
      U22_A(x1,x2,x3) = x1 + x3 + (1,1)
      U23_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x3 + (13,1)
      U24_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (12,1)
      U25_A(x1,x2) = x2 + (11,1)
      isList_A(x1) = ((1,0),(1,0)) x1 + (9,1)
      U26_A(x1) = x1 + (1,1)
      U31_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + (4,1)
      U32_A(x1,x2) = x2 + (3,1)
      U33_A(x1) = x1 + (1,1)
      isQid_A(x1) = x1 + (1,1)
      U41_A(x1,x2,x3) = x2 + ((1,0),(1,0)) x3 + (11,1)
      U42_A(x1,x2,x3) = ((1,0),(1,0)) x2 + x3 + (10,1)
      U43_A(x1,x2,x3) = ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (9,1)
      U44_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x3 + (8,1)
      U45_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + (7,1)
      U46_A(x1) = x1 + (1,1)
      U51_A(x1,x2,x3) = ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (7,1)
      U52_A(x1,x2,x3) = x1 + ((1,0),(1,0)) x3 + (5,1)
      U53_A(x1,x2,x3) = ((0,0),(1,0)) x2 + ((0,0),(1,0)) x3 + (17,0)
      U54_A(x1,x2,x3) = ((0,0),(1,0)) x2 + (16,1)
      U55_A(x1,x2) = (15,1)
      U56_A(x1) = (14,1)
      U61_A(x1,x2) = ((1,0),(1,0)) x1 + (3,1)
      U62_A(x1,x2) = ((0,0),(1,0)) x2 + (15,0)
      U63_A(x1) = (14,1)
      U71_A(x1,x2,x3) = ((0,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (17,1)
      U72_A(x1,x2) = ((1,0),(1,0)) x2 + (16,0)
      U73_A(x1,x2) = (15,1)
      isPal_A(x1) = ((1,0),(1,0)) x1 + (17,1)
      U74_A(x1) = (14,1)
      U81_A(x1,x2) = x2 + (16,1)
      U82_A(x1,x2) = ((1,0),(1,0)) x2 + (15,1)
      U83_A(x1) = (14,1)
      isNePal_A(x1) = ((1,0),(1,0)) x1 + (5,1)
      U91_A(x1,x2) = ((1,0),(1,0)) x2 + (3,1)
      a_A() = (13,0)
      e_A() = (13,0)
      i_A() = (13,1)
      o_A() = (13,1)
      u_A() = (13,1)

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: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(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, r231, r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      active#_A(x1) = x1
      ___A(x1,x2) = ((1,0),(1,0)) x1 + x2 + (5,1)
      mark#_A(x1) = x1 + (0,3)
      mark_A(x1) = x1 + (0,2)
      active_A(x1) = x1
      nil_A() = (2,0)
      U11_A(x1,x2) = ((1,0),(1,0)) x1 + (3,1)
      tt_A() = (1,2)
      U12_A(x1,x2) = ((0,0),(1,0)) x2 + (3,1)
      isPalListKind_A(x1) = ((0,0),(1,0)) x1 + (4,1)
      U13_A(x1) = ((0,0),(1,0)) x1 + (2,1)
      isNeList_A(x1) = ((1,0),(1,1)) x1 + (12,5)
      U21_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (10,1)
      U22_A(x1,x2,x3) = ((1,0),(1,0)) x2 + ((1,0),(1,0)) x3 + (9,1)
      U23_A(x1,x2,x3) = x2 + ((1,0),(1,1)) x3 + (8,1)
      U24_A(x1,x2,x3) = x1 + ((0,0),(1,0)) x2 + ((0,0),(1,0)) x3 + (3,1)
      U25_A(x1,x2) = (3,2)
      isList_A(x1) = ((1,0),(1,0)) x1 + (8,1)
      U26_A(x1) = (2,1)
      U31_A(x1,x2) = (5,4)
      U32_A(x1,x2) = (4,3)
      U33_A(x1) = ((1,0),(1,0)) x1 + (1,1)
      isQid_A(x1) = (2,3)
      U41_A(x1,x2,x3) = ((0,0),(1,0)) x1 + x3 + (7,6)
      U42_A(x1,x2,x3) = ((0,0),(1,0)) x2 + x3 + (6,1)
      U43_A(x1,x2,x3) = ((1,0),(1,1)) x3 + (5,1)
      U44_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (4,1)
      U45_A(x1,x2) = (3,1)
      U46_A(x1) = ((0,0),(1,0)) x1 + (2,1)
      U51_A(x1,x2,x3) = x1 + x3 + (12,8)
      U52_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((1,0),(1,0)) x3 + (12,1)
      U53_A(x1,x2,x3) = x1 + x3 + (7,1)
      U54_A(x1,x2,x3) = x1 + (3,13)
      U55_A(x1,x2) = (3,12)
      U56_A(x1) = ((0,0),(1,0)) x1 + (2,1)
      U61_A(x1,x2) = ((1,0),(1,0)) x1 + (3,1)
      U62_A(x1,x2) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + (3,1)
      U63_A(x1) = (2,1)
      U71_A(x1,x2,x3) = x3 + (8,19)
      U72_A(x1,x2) = x2 + (7,18)
      U73_A(x1,x2) = x2 + (6,4)
      isPal_A(x1) = x1 + (8,5)
      U74_A(x1) = x1 + (1,1)
      U81_A(x1,x2) = x1 + (3,3)
      U82_A(x1,x2) = ((0,0),(1,0)) x2 + (3,1)
      U83_A(x1) = (2,1)
      isNePal_A(x1) = ((1,0),(1,1)) x1 + (8,8)
      U91_A(x1,x2) = ((0,0),(1,0)) x2 + (3,5)
      U92_A(x1) = (2,5)
      a_A() = (1,1)
      e_A() = (1,0)
      i_A() = (1,1)
      o_A() = (4,0)
      u_A() = (4,1)

The next rules are strictly ordered:

  p1, p2

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: __#(X1,active(X2)) -> __#(X1,X2)
p3: __#(active(X1),X2) -> __#(X1,X2)
p4: __#(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      __#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(X1,active(X2)) -> U12#(X1,X2)
p3: U12#(active(X1),X2) -> U12#(X1,X2)
p4: U12#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U12#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(mark(X)) -> isPalListKind#(X)
p2: isPalListKind#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      isPalListKind#_A(x1) = ((1,0),(1,1)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U13#_A(x1) = x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(mark(X)) -> isNeList#(X)
p2: isNeList#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      isNeList#_A(x1) = ((1,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,X2,active(X3)) -> U22#(X1,X2,X3)
p3: U22#(X1,active(X2),X3) -> U22#(X1,X2,X3)
p4: U22#(active(X1),X2,X3) -> U22#(X1,X2,X3)
p5: U22#(X1,X2,mark(X3)) -> U22#(X1,X2,X3)
p6: U22#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U22#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U23#(X1,X2,X3)
p3: U23#(X1,active(X2),X3) -> U23#(X1,X2,X3)
p4: U23#(active(X1),X2,X3) -> U23#(X1,X2,X3)
p5: U23#(X1,X2,mark(X3)) -> U23#(X1,X2,X3)
p6: U23#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U23#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U24#(X1,X2,X3)
p3: U24#(X1,active(X2),X3) -> U24#(X1,X2,X3)
p4: U24#(active(X1),X2,X3) -> U24#(X1,X2,X3)
p5: U24#(X1,X2,mark(X3)) -> U24#(X1,X2,X3)
p6: U24#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U24#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,active(X2)) -> U25#(X1,X2)
p3: U25#(active(X1),X2) -> U25#(X1,X2)
p4: U25#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U25#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(mark(X)) -> isList#(X)
p2: isList#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      isList#_A(x1) = x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U26#_A(x1) = ((1,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,active(X2)) -> U32#(X1,X2)
p3: U32#(active(X1),X2) -> U32#(X1,X2)
p4: U32#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U32#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U33#_A(x1) = ((1,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(mark(X)) -> isQid#(X)
p2: isQid#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      isQid#_A(x1) = ((1,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,X2,active(X3)) -> U42#(X1,X2,X3)
p3: U42#(X1,active(X2),X3) -> U42#(X1,X2,X3)
p4: U42#(active(X1),X2,X3) -> U42#(X1,X2,X3)
p5: U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3)
p6: U42#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U42#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U43#(X1,X2,X3)
p3: U43#(X1,active(X2),X3) -> U43#(X1,X2,X3)
p4: U43#(active(X1),X2,X3) -> U43#(X1,X2,X3)
p5: U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3)
p6: U43#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U43#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U44#(X1,X2,X3)
p3: U44#(X1,active(X2),X3) -> U44#(X1,X2,X3)
p4: U44#(active(X1),X2,X3) -> U44#(X1,X2,X3)
p5: U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3)
p6: U44#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U44#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,active(X2)) -> U45#(X1,X2)
p3: U45#(active(X1),X2) -> U45#(X1,X2)
p4: U45#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U45#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U46#_A(x1) = ((1,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,X2,active(X3)) -> U52#(X1,X2,X3)
p3: U52#(X1,active(X2),X3) -> U52#(X1,X2,X3)
p4: U52#(active(X1),X2,X3) -> U52#(X1,X2,X3)
p5: U52#(X1,X2,mark(X3)) -> U52#(X1,X2,X3)
p6: U52#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U52#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U53#(X1,X2,X3)
p3: U53#(X1,active(X2),X3) -> U53#(X1,X2,X3)
p4: U53#(active(X1),X2,X3) -> U53#(X1,X2,X3)
p5: U53#(X1,X2,mark(X3)) -> U53#(X1,X2,X3)
p6: U53#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U53#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U54#(X1,X2,X3)
p3: U54#(X1,active(X2),X3) -> U54#(X1,X2,X3)
p4: U54#(active(X1),X2,X3) -> U54#(X1,X2,X3)
p5: U54#(X1,X2,mark(X3)) -> U54#(X1,X2,X3)
p6: U54#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U54#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,active(X2)) -> U55#(X1,X2)
p3: U55#(active(X1),X2) -> U55#(X1,X2)
p4: U55#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U55#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U56#_A(x1) = ((1,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,active(X2)) -> U62#(X1,X2)
p3: U62#(active(X1),X2) -> U62#(X1,X2)
p4: U62#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U62#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U63#_A(x1) = x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,active(X2)) -> U72#(X1,X2)
p3: U72#(active(X1),X2) -> U72#(X1,X2)
p4: U72#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U72#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(X1,active(X2)) -> U73#(X1,X2)
p3: U73#(active(X1),X2) -> U73#(X1,X2)
p4: U73#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U73#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(mark(X)) -> isPal#(X)
p2: isPal#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      isPal#_A(x1) = ((0,0),(1,0)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U74#_A(x1) = x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,active(X2)) -> U82#(X1,X2)
p3: U82#(active(X1),X2) -> U82#(X1,X2)
p4: U82#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U82#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U83#_A(x1) = ((1,0),(1,1)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(mark(X)) -> isNePal#(X)
p2: isNePal#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      isNePal#_A(x1) = ((1,0),(1,1)) x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(active(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U92#_A(x1) = x1
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2

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#(X1,active(X2)) -> U11#(X1,X2)
p3: U11#(active(X1),X2) -> U11#(X1,X2)
p4: U11#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U11#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
p3: U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
p4: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
p5: U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
p6: U21#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U21#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,active(X2)) -> U31#(X1,X2)
p3: U31#(active(X1),X2) -> U31#(X1,X2)
p4: U31#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U31#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
p3: U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
p4: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
p5: U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
p6: U41#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U41#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
p3: U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
p4: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
p5: U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
p6: U51#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U51#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,active(X2)) -> U61#(X1,X2)
p3: U61#(active(X1),X2) -> U61#(X1,X2)
p4: U61#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U61#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(X1,X2,active(X3)) -> U71#(X1,X2,X3)
p3: U71#(X1,active(X2),X3) -> U71#(X1,X2,X3)
p4: U71#(active(X1),X2,X3) -> U71#(X1,X2,X3)
p5: U71#(X1,X2,mark(X3)) -> U71#(X1,X2,X3)
p6: U71#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U71#_A(x1,x2,x3) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + ((1,0),(1,1)) x3
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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#(X1,active(X2)) -> U81#(X1,X2)
p3: U81#(active(X1),X2) -> U81#(X1,X2)
p4: U81#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U81#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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#(X1,active(X2)) -> U91#(X1,X2)
p3: U91#(active(X1),X2) -> U91#(X1,X2)
p4: U91#(X1,mark(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: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r63: mark(nil()) -> active(nil())
r64: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r65: mark(tt()) -> active(tt())
r66: mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
r67: mark(isPalListKind(X)) -> active(isPalListKind(X))
r68: mark(U13(X)) -> active(U13(mark(X)))
r69: mark(isNeList(X)) -> active(isNeList(X))
r70: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r71: mark(U22(X1,X2,X3)) -> active(U22(mark(X1),X2,X3))
r72: mark(U23(X1,X2,X3)) -> active(U23(mark(X1),X2,X3))
r73: mark(U24(X1,X2,X3)) -> active(U24(mark(X1),X2,X3))
r74: mark(U25(X1,X2)) -> active(U25(mark(X1),X2))
r75: mark(isList(X)) -> active(isList(X))
r76: mark(U26(X)) -> active(U26(mark(X)))
r77: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r78: mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
r79: mark(U33(X)) -> active(U33(mark(X)))
r80: mark(isQid(X)) -> active(isQid(X))
r81: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r82: mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3))
r83: mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3))
r84: mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3))
r85: mark(U45(X1,X2)) -> active(U45(mark(X1),X2))
r86: mark(U46(X)) -> active(U46(mark(X)))
r87: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r88: mark(U52(X1,X2,X3)) -> active(U52(mark(X1),X2,X3))
r89: mark(U53(X1,X2,X3)) -> active(U53(mark(X1),X2,X3))
r90: mark(U54(X1,X2,X3)) -> active(U54(mark(X1),X2,X3))
r91: mark(U55(X1,X2)) -> active(U55(mark(X1),X2))
r92: mark(U56(X)) -> active(U56(mark(X)))
r93: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r94: mark(U62(X1,X2)) -> active(U62(mark(X1),X2))
r95: mark(U63(X)) -> active(U63(mark(X)))
r96: mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
r97: mark(U72(X1,X2)) -> active(U72(mark(X1),X2))
r98: mark(U73(X1,X2)) -> active(U73(mark(X1),X2))
r99: mark(isPal(X)) -> active(isPal(X))
r100: mark(U74(X)) -> active(U74(mark(X)))
r101: mark(U81(X1,X2)) -> active(U81(mark(X1),X2))
r102: mark(U82(X1,X2)) -> active(U82(mark(X1),X2))
r103: mark(U83(X)) -> active(U83(mark(X)))
r104: mark(isNePal(X)) -> active(isNePal(X))
r105: mark(U91(X1,X2)) -> active(U91(mark(X1),X2))
r106: mark(U92(X)) -> active(U92(mark(X)))
r107: mark(a()) -> active(a())
r108: mark(e()) -> active(e())
r109: mark(i()) -> active(i())
r110: mark(o()) -> active(o())
r111: mark(u()) -> active(u())
r112: __(mark(X1),X2) -> __(X1,X2)
r113: __(X1,mark(X2)) -> __(X1,X2)
r114: __(active(X1),X2) -> __(X1,X2)
r115: __(X1,active(X2)) -> __(X1,X2)
r116: U11(mark(X1),X2) -> U11(X1,X2)
r117: U11(X1,mark(X2)) -> U11(X1,X2)
r118: U11(active(X1),X2) -> U11(X1,X2)
r119: U11(X1,active(X2)) -> U11(X1,X2)
r120: U12(mark(X1),X2) -> U12(X1,X2)
r121: U12(X1,mark(X2)) -> U12(X1,X2)
r122: U12(active(X1),X2) -> U12(X1,X2)
r123: U12(X1,active(X2)) -> U12(X1,X2)
r124: isPalListKind(mark(X)) -> isPalListKind(X)
r125: isPalListKind(active(X)) -> isPalListKind(X)
r126: U13(mark(X)) -> U13(X)
r127: U13(active(X)) -> U13(X)
r128: isNeList(mark(X)) -> isNeList(X)
r129: isNeList(active(X)) -> isNeList(X)
r130: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r131: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r132: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r133: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r134: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r135: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r136: U22(mark(X1),X2,X3) -> U22(X1,X2,X3)
r137: U22(X1,mark(X2),X3) -> U22(X1,X2,X3)
r138: U22(X1,X2,mark(X3)) -> U22(X1,X2,X3)
r139: U22(active(X1),X2,X3) -> U22(X1,X2,X3)
r140: U22(X1,active(X2),X3) -> U22(X1,X2,X3)
r141: U22(X1,X2,active(X3)) -> U22(X1,X2,X3)
r142: U23(mark(X1),X2,X3) -> U23(X1,X2,X3)
r143: U23(X1,mark(X2),X3) -> U23(X1,X2,X3)
r144: U23(X1,X2,mark(X3)) -> U23(X1,X2,X3)
r145: U23(active(X1),X2,X3) -> U23(X1,X2,X3)
r146: U23(X1,active(X2),X3) -> U23(X1,X2,X3)
r147: U23(X1,X2,active(X3)) -> U23(X1,X2,X3)
r148: U24(mark(X1),X2,X3) -> U24(X1,X2,X3)
r149: U24(X1,mark(X2),X3) -> U24(X1,X2,X3)
r150: U24(X1,X2,mark(X3)) -> U24(X1,X2,X3)
r151: U24(active(X1),X2,X3) -> U24(X1,X2,X3)
r152: U24(X1,active(X2),X3) -> U24(X1,X2,X3)
r153: U24(X1,X2,active(X3)) -> U24(X1,X2,X3)
r154: U25(mark(X1),X2) -> U25(X1,X2)
r155: U25(X1,mark(X2)) -> U25(X1,X2)
r156: U25(active(X1),X2) -> U25(X1,X2)
r157: U25(X1,active(X2)) -> U25(X1,X2)
r158: isList(mark(X)) -> isList(X)
r159: isList(active(X)) -> isList(X)
r160: U26(mark(X)) -> U26(X)
r161: U26(active(X)) -> U26(X)
r162: U31(mark(X1),X2) -> U31(X1,X2)
r163: U31(X1,mark(X2)) -> U31(X1,X2)
r164: U31(active(X1),X2) -> U31(X1,X2)
r165: U31(X1,active(X2)) -> U31(X1,X2)
r166: U32(mark(X1),X2) -> U32(X1,X2)
r167: U32(X1,mark(X2)) -> U32(X1,X2)
r168: U32(active(X1),X2) -> U32(X1,X2)
r169: U32(X1,active(X2)) -> U32(X1,X2)
r170: U33(mark(X)) -> U33(X)
r171: U33(active(X)) -> U33(X)
r172: isQid(mark(X)) -> isQid(X)
r173: isQid(active(X)) -> isQid(X)
r174: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r175: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r176: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r177: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r178: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r179: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r180: U42(mark(X1),X2,X3) -> U42(X1,X2,X3)
r181: U42(X1,mark(X2),X3) -> U42(X1,X2,X3)
r182: U42(X1,X2,mark(X3)) -> U42(X1,X2,X3)
r183: U42(active(X1),X2,X3) -> U42(X1,X2,X3)
r184: U42(X1,active(X2),X3) -> U42(X1,X2,X3)
r185: U42(X1,X2,active(X3)) -> U42(X1,X2,X3)
r186: U43(mark(X1),X2,X3) -> U43(X1,X2,X3)
r187: U43(X1,mark(X2),X3) -> U43(X1,X2,X3)
r188: U43(X1,X2,mark(X3)) -> U43(X1,X2,X3)
r189: U43(active(X1),X2,X3) -> U43(X1,X2,X3)
r190: U43(X1,active(X2),X3) -> U43(X1,X2,X3)
r191: U43(X1,X2,active(X3)) -> U43(X1,X2,X3)
r192: U44(mark(X1),X2,X3) -> U44(X1,X2,X3)
r193: U44(X1,mark(X2),X3) -> U44(X1,X2,X3)
r194: U44(X1,X2,mark(X3)) -> U44(X1,X2,X3)
r195: U44(active(X1),X2,X3) -> U44(X1,X2,X3)
r196: U44(X1,active(X2),X3) -> U44(X1,X2,X3)
r197: U44(X1,X2,active(X3)) -> U44(X1,X2,X3)
r198: U45(mark(X1),X2) -> U45(X1,X2)
r199: U45(X1,mark(X2)) -> U45(X1,X2)
r200: U45(active(X1),X2) -> U45(X1,X2)
r201: U45(X1,active(X2)) -> U45(X1,X2)
r202: U46(mark(X)) -> U46(X)
r203: U46(active(X)) -> U46(X)
r204: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r205: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r206: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r207: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r208: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r209: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r210: U52(mark(X1),X2,X3) -> U52(X1,X2,X3)
r211: U52(X1,mark(X2),X3) -> U52(X1,X2,X3)
r212: U52(X1,X2,mark(X3)) -> U52(X1,X2,X3)
r213: U52(active(X1),X2,X3) -> U52(X1,X2,X3)
r214: U52(X1,active(X2),X3) -> U52(X1,X2,X3)
r215: U52(X1,X2,active(X3)) -> U52(X1,X2,X3)
r216: U53(mark(X1),X2,X3) -> U53(X1,X2,X3)
r217: U53(X1,mark(X2),X3) -> U53(X1,X2,X3)
r218: U53(X1,X2,mark(X3)) -> U53(X1,X2,X3)
r219: U53(active(X1),X2,X3) -> U53(X1,X2,X3)
r220: U53(X1,active(X2),X3) -> U53(X1,X2,X3)
r221: U53(X1,X2,active(X3)) -> U53(X1,X2,X3)
r222: U54(mark(X1),X2,X3) -> U54(X1,X2,X3)
r223: U54(X1,mark(X2),X3) -> U54(X1,X2,X3)
r224: U54(X1,X2,mark(X3)) -> U54(X1,X2,X3)
r225: U54(active(X1),X2,X3) -> U54(X1,X2,X3)
r226: U54(X1,active(X2),X3) -> U54(X1,X2,X3)
r227: U54(X1,X2,active(X3)) -> U54(X1,X2,X3)
r228: U55(mark(X1),X2) -> U55(X1,X2)
r229: U55(X1,mark(X2)) -> U55(X1,X2)
r230: U55(active(X1),X2) -> U55(X1,X2)
r231: U55(X1,active(X2)) -> U55(X1,X2)
r232: U56(mark(X)) -> U56(X)
r233: U56(active(X)) -> U56(X)
r234: U61(mark(X1),X2) -> U61(X1,X2)
r235: U61(X1,mark(X2)) -> U61(X1,X2)
r236: U61(active(X1),X2) -> U61(X1,X2)
r237: U61(X1,active(X2)) -> U61(X1,X2)
r238: U62(mark(X1),X2) -> U62(X1,X2)
r239: U62(X1,mark(X2)) -> U62(X1,X2)
r240: U62(active(X1),X2) -> U62(X1,X2)
r241: U62(X1,active(X2)) -> U62(X1,X2)
r242: U63(mark(X)) -> U63(X)
r243: U63(active(X)) -> U63(X)
r244: U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
r245: U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
r246: U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
r247: U71(active(X1),X2,X3) -> U71(X1,X2,X3)
r248: U71(X1,active(X2),X3) -> U71(X1,X2,X3)
r249: U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
r250: U72(mark(X1),X2) -> U72(X1,X2)
r251: U72(X1,mark(X2)) -> U72(X1,X2)
r252: U72(active(X1),X2) -> U72(X1,X2)
r253: U72(X1,active(X2)) -> U72(X1,X2)
r254: U73(mark(X1),X2) -> U73(X1,X2)
r255: U73(X1,mark(X2)) -> U73(X1,X2)
r256: U73(active(X1),X2) -> U73(X1,X2)
r257: U73(X1,active(X2)) -> U73(X1,X2)
r258: isPal(mark(X)) -> isPal(X)
r259: isPal(active(X)) -> isPal(X)
r260: U74(mark(X)) -> U74(X)
r261: U74(active(X)) -> U74(X)
r262: U81(mark(X1),X2) -> U81(X1,X2)
r263: U81(X1,mark(X2)) -> U81(X1,X2)
r264: U81(active(X1),X2) -> U81(X1,X2)
r265: U81(X1,active(X2)) -> U81(X1,X2)
r266: U82(mark(X1),X2) -> U82(X1,X2)
r267: U82(X1,mark(X2)) -> U82(X1,X2)
r268: U82(active(X1),X2) -> U82(X1,X2)
r269: U82(X1,active(X2)) -> U82(X1,X2)
r270: U83(mark(X)) -> U83(X)
r271: U83(active(X)) -> U83(X)
r272: isNePal(mark(X)) -> isNePal(X)
r273: isNePal(active(X)) -> isNePal(X)
r274: U91(mark(X1),X2) -> U91(X1,X2)
r275: U91(X1,mark(X2)) -> U91(X1,X2)
r276: U91(active(X1),X2) -> U91(X1,X2)
r277: U91(X1,active(X2)) -> U91(X1,X2)
r278: U92(mark(X)) -> U92(X)
r279: U92(active(X)) -> U92(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      U91#_A(x1,x2) = ((1,0),(1,1)) x1 + x2
      mark_A(x1) = ((1,0),(1,1)) x1 + (1,1)
      active_A(x1) = ((1,0),(1,1)) x1 + (1,1)

The next rules are strictly ordered:

  p1, p2, p3, p4
  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, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, r276, r277, r278, r279

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