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(isNeList(V)))
  active(U12(tt())) -> mark(tt())
  active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
  active(U22(tt(),V2)) -> mark(U23(isList(V2)))
  active(U23(tt())) -> mark(tt())
  active(U31(tt(),V)) -> mark(U32(isQid(V)))
  active(U32(tt())) -> mark(tt())
  active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
  active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
  active(U43(tt())) -> mark(tt())
  active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
  active(U52(tt(),V2)) -> mark(U53(isList(V2)))
  active(U53(tt())) -> mark(tt())
  active(U61(tt(),V)) -> mark(U62(isQid(V)))
  active(U62(tt())) -> mark(tt())
  active(U71(tt(),V)) -> mark(U72(isNePal(V)))
  active(U72(tt())) -> mark(tt())
  active(and(tt(),X)) -> mark(X)
  active(isList(V)) -> mark(U11(isPalListKind(V),V))
  active(isList(nil())) -> mark(tt())
  active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
  active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
  active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
  active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
  active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
  active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
  active(isPal(V)) -> mark(U71(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(and(isPalListKind(V1),isPalListKind(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(X)) -> active(U12(mark(X)))
  mark(isNeList(X)) -> active(isNeList(X))
  mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
  mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
  mark(isList(X)) -> active(isList(X))
  mark(U23(X)) -> active(U23(mark(X)))
  mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
  mark(U32(X)) -> active(U32(mark(X)))
  mark(isQid(X)) -> active(isQid(X))
  mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
  mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
  mark(U43(X)) -> active(U43(mark(X)))
  mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
  mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
  mark(U53(X)) -> active(U53(mark(X)))
  mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
  mark(U62(X)) -> active(U62(mark(X)))
  mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
  mark(U72(X)) -> active(U72(mark(X)))
  mark(isNePal(X)) -> active(isNePal(X))
  mark(and(X1,X2)) -> active(and(mark(X1),X2))
  mark(isPalListKind(X)) -> active(isPalListKind(X))
  mark(isPal(X)) -> active(isPal(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(X)) -> U12(X)
  U12(active(X)) -> U12(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) -> U22(X1,X2)
  U22(X1,mark(X2)) -> U22(X1,X2)
  U22(active(X1),X2) -> U22(X1,X2)
  U22(X1,active(X2)) -> U22(X1,X2)
  isList(mark(X)) -> isList(X)
  isList(active(X)) -> isList(X)
  U23(mark(X)) -> U23(X)
  U23(active(X)) -> U23(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(X)) -> U32(X)
  U32(active(X)) -> U32(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) -> U42(X1,X2)
  U42(X1,mark(X2)) -> U42(X1,X2)
  U42(active(X1),X2) -> U42(X1,X2)
  U42(X1,active(X2)) -> U42(X1,X2)
  U43(mark(X)) -> U43(X)
  U43(active(X)) -> U43(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) -> U52(X1,X2)
  U52(X1,mark(X2)) -> U52(X1,X2)
  U52(active(X1),X2) -> U52(X1,X2)
  U52(X1,active(X2)) -> U52(X1,X2)
  U53(mark(X)) -> U53(X)
  U53(active(X)) -> U53(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(X)) -> U62(X)
  U62(active(X)) -> U62(X)
  U71(mark(X1),X2) -> U71(X1,X2)
  U71(X1,mark(X2)) -> U71(X1,X2)
  U71(active(X1),X2) -> U71(X1,X2)
  U71(X1,active(X2)) -> U71(X1,X2)
  U72(mark(X)) -> U72(X)
  U72(active(X)) -> U72(X)
  isNePal(mark(X)) -> isNePal(X)
  isNePal(active(X)) -> isNePal(X)
  and(mark(X1),X2) -> and(X1,X2)
  and(X1,mark(X2)) -> and(X1,X2)
  and(active(X1),X2) -> and(X1,X2)
  and(X1,active(X2)) -> and(X1,X2)
  isPalListKind(mark(X)) -> isPalListKind(X)
  isPalListKind(active(X)) -> isPalListKind(X)
  isPal(mark(X)) -> isPal(X)
  isPal(active(X)) -> isPal(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(isNeList(V)))
p7: active#(U11(tt(),V)) -> U12#(isNeList(V))
p8: active#(U11(tt(),V)) -> isNeList#(V)
p9: active#(U12(tt())) -> mark#(tt())
p10: active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2))
p11: active#(U21(tt(),V1,V2)) -> U22#(isList(V1),V2)
p12: active#(U21(tt(),V1,V2)) -> isList#(V1)
p13: active#(U22(tt(),V2)) -> mark#(U23(isList(V2)))
p14: active#(U22(tt(),V2)) -> U23#(isList(V2))
p15: active#(U22(tt(),V2)) -> isList#(V2)
p16: active#(U23(tt())) -> mark#(tt())
p17: active#(U31(tt(),V)) -> mark#(U32(isQid(V)))
p18: active#(U31(tt(),V)) -> U32#(isQid(V))
p19: active#(U31(tt(),V)) -> isQid#(V)
p20: active#(U32(tt())) -> mark#(tt())
p21: active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2))
p22: active#(U41(tt(),V1,V2)) -> U42#(isList(V1),V2)
p23: active#(U41(tt(),V1,V2)) -> isList#(V1)
p24: active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2)))
p25: active#(U42(tt(),V2)) -> U43#(isNeList(V2))
p26: active#(U42(tt(),V2)) -> isNeList#(V2)
p27: active#(U43(tt())) -> mark#(tt())
p28: active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2))
p29: active#(U51(tt(),V1,V2)) -> U52#(isNeList(V1),V2)
p30: active#(U51(tt(),V1,V2)) -> isNeList#(V1)
p31: active#(U52(tt(),V2)) -> mark#(U53(isList(V2)))
p32: active#(U52(tt(),V2)) -> U53#(isList(V2))
p33: active#(U52(tt(),V2)) -> isList#(V2)
p34: active#(U53(tt())) -> mark#(tt())
p35: active#(U61(tt(),V)) -> mark#(U62(isQid(V)))
p36: active#(U61(tt(),V)) -> U62#(isQid(V))
p37: active#(U61(tt(),V)) -> isQid#(V)
p38: active#(U62(tt())) -> mark#(tt())
p39: active#(U71(tt(),V)) -> mark#(U72(isNePal(V)))
p40: active#(U71(tt(),V)) -> U72#(isNePal(V))
p41: active#(U71(tt(),V)) -> isNePal#(V)
p42: active#(U72(tt())) -> mark#(tt())
p43: active#(and(tt(),X)) -> mark#(X)
p44: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p45: active#(isList(V)) -> U11#(isPalListKind(V),V)
p46: active#(isList(V)) -> isPalListKind#(V)
p47: active#(isList(nil())) -> mark#(tt())
p48: active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
p49: active#(isList(__(V1,V2))) -> U21#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)
p50: active#(isList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2))
p51: active#(isList(__(V1,V2))) -> isPalListKind#(V1)
p52: active#(isList(__(V1,V2))) -> isPalListKind#(V2)
p53: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p54: active#(isNeList(V)) -> U31#(isPalListKind(V),V)
p55: active#(isNeList(V)) -> isPalListKind#(V)
p56: active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
p57: active#(isNeList(__(V1,V2))) -> U41#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)
p58: active#(isNeList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2))
p59: active#(isNeList(__(V1,V2))) -> isPalListKind#(V1)
p60: active#(isNeList(__(V1,V2))) -> isPalListKind#(V2)
p61: active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
p62: active#(isNeList(__(V1,V2))) -> U51#(and(isPalListKind(V1),isPalListKind(V2)),V1,V2)
p63: active#(isNeList(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2))
p64: active#(isNeList(__(V1,V2))) -> isPalListKind#(V1)
p65: active#(isNeList(__(V1,V2))) -> isPalListKind#(V2)
p66: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p67: active#(isNePal(V)) -> U61#(isPalListKind(V),V)
p68: active#(isNePal(V)) -> isPalListKind#(V)
p69: active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
p70: active#(isNePal(__(I,__(P,I)))) -> and#(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
p71: active#(isNePal(__(I,__(P,I)))) -> and#(isQid(I),isPalListKind(I))
p72: active#(isNePal(__(I,__(P,I)))) -> isQid#(I)
p73: active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(I)
p74: active#(isNePal(__(I,__(P,I)))) -> and#(isPal(P),isPalListKind(P))
p75: active#(isNePal(__(I,__(P,I)))) -> isPal#(P)
p76: active#(isNePal(__(I,__(P,I)))) -> isPalListKind#(P)
p77: active#(isPal(V)) -> mark#(U71(isPalListKind(V),V))
p78: active#(isPal(V)) -> U71#(isPalListKind(V),V)
p79: active#(isPal(V)) -> isPalListKind#(V)
p80: active#(isPal(nil())) -> mark#(tt())
p81: active#(isPalListKind(a())) -> mark#(tt())
p82: active#(isPalListKind(e())) -> mark#(tt())
p83: active#(isPalListKind(i())) -> mark#(tt())
p84: active#(isPalListKind(nil())) -> mark#(tt())
p85: active#(isPalListKind(o())) -> mark#(tt())
p86: active#(isPalListKind(u())) -> mark#(tt())
p87: active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2)))
p88: active#(isPalListKind(__(V1,V2))) -> and#(isPalListKind(V1),isPalListKind(V2))
p89: active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V1)
p90: active#(isPalListKind(__(V1,V2))) -> isPalListKind#(V2)
p91: active#(isQid(a())) -> mark#(tt())
p92: active#(isQid(e())) -> mark#(tt())
p93: active#(isQid(i())) -> mark#(tt())
p94: active#(isQid(o())) -> mark#(tt())
p95: active#(isQid(u())) -> mark#(tt())
p96: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))
p97: mark#(__(X1,X2)) -> __#(mark(X1),mark(X2))
p98: mark#(__(X1,X2)) -> mark#(X1)
p99: mark#(__(X1,X2)) -> mark#(X2)
p100: mark#(nil()) -> active#(nil())
p101: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p102: mark#(U11(X1,X2)) -> U11#(mark(X1),X2)
p103: mark#(U11(X1,X2)) -> mark#(X1)
p104: mark#(tt()) -> active#(tt())
p105: mark#(U12(X)) -> active#(U12(mark(X)))
p106: mark#(U12(X)) -> U12#(mark(X))
p107: mark#(U12(X)) -> mark#(X)
p108: mark#(isNeList(X)) -> active#(isNeList(X))
p109: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p110: mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3)
p111: mark#(U21(X1,X2,X3)) -> mark#(X1)
p112: mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
p113: mark#(U22(X1,X2)) -> U22#(mark(X1),X2)
p114: mark#(U22(X1,X2)) -> mark#(X1)
p115: mark#(isList(X)) -> active#(isList(X))
p116: mark#(U23(X)) -> active#(U23(mark(X)))
p117: mark#(U23(X)) -> U23#(mark(X))
p118: mark#(U23(X)) -> mark#(X)
p119: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p120: mark#(U31(X1,X2)) -> U31#(mark(X1),X2)
p121: mark#(U31(X1,X2)) -> mark#(X1)
p122: mark#(U32(X)) -> active#(U32(mark(X)))
p123: mark#(U32(X)) -> U32#(mark(X))
p124: mark#(U32(X)) -> mark#(X)
p125: mark#(isQid(X)) -> active#(isQid(X))
p126: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p127: mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3)
p128: mark#(U41(X1,X2,X3)) -> mark#(X1)
p129: mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2))
p130: mark#(U42(X1,X2)) -> U42#(mark(X1),X2)
p131: mark#(U42(X1,X2)) -> mark#(X1)
p132: mark#(U43(X)) -> active#(U43(mark(X)))
p133: mark#(U43(X)) -> U43#(mark(X))
p134: mark#(U43(X)) -> mark#(X)
p135: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p136: mark#(U51(X1,X2,X3)) -> U51#(mark(X1),X2,X3)
p137: mark#(U51(X1,X2,X3)) -> mark#(X1)
p138: mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2))
p139: mark#(U52(X1,X2)) -> U52#(mark(X1),X2)
p140: mark#(U52(X1,X2)) -> mark#(X1)
p141: mark#(U53(X)) -> active#(U53(mark(X)))
p142: mark#(U53(X)) -> U53#(mark(X))
p143: mark#(U53(X)) -> mark#(X)
p144: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p145: mark#(U61(X1,X2)) -> U61#(mark(X1),X2)
p146: mark#(U61(X1,X2)) -> mark#(X1)
p147: mark#(U62(X)) -> active#(U62(mark(X)))
p148: mark#(U62(X)) -> U62#(mark(X))
p149: mark#(U62(X)) -> mark#(X)
p150: mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
p151: mark#(U71(X1,X2)) -> U71#(mark(X1),X2)
p152: mark#(U71(X1,X2)) -> mark#(X1)
p153: mark#(U72(X)) -> active#(U72(mark(X)))
p154: mark#(U72(X)) -> U72#(mark(X))
p155: mark#(U72(X)) -> mark#(X)
p156: mark#(isNePal(X)) -> active#(isNePal(X))
p157: mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
p158: mark#(and(X1,X2)) -> and#(mark(X1),X2)
p159: mark#(and(X1,X2)) -> mark#(X1)
p160: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p161: mark#(isPal(X)) -> active#(isPal(X))
p162: mark#(a()) -> active#(a())
p163: mark#(e()) -> active#(e())
p164: mark#(i()) -> active#(i())
p165: mark#(o()) -> active#(o())
p166: mark#(u()) -> active#(u())
p167: __#(mark(X1),X2) -> __#(X1,X2)
p168: __#(X1,mark(X2)) -> __#(X1,X2)
p169: __#(active(X1),X2) -> __#(X1,X2)
p170: __#(X1,active(X2)) -> __#(X1,X2)
p171: U11#(mark(X1),X2) -> U11#(X1,X2)
p172: U11#(X1,mark(X2)) -> U11#(X1,X2)
p173: U11#(active(X1),X2) -> U11#(X1,X2)
p174: U11#(X1,active(X2)) -> U11#(X1,X2)
p175: U12#(mark(X)) -> U12#(X)
p176: U12#(active(X)) -> U12#(X)
p177: isNeList#(mark(X)) -> isNeList#(X)
p178: isNeList#(active(X)) -> isNeList#(X)
p179: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
p180: U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
p181: U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
p182: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
p183: U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
p184: U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
p185: U22#(mark(X1),X2) -> U22#(X1,X2)
p186: U22#(X1,mark(X2)) -> U22#(X1,X2)
p187: U22#(active(X1),X2) -> U22#(X1,X2)
p188: U22#(X1,active(X2)) -> U22#(X1,X2)
p189: isList#(mark(X)) -> isList#(X)
p190: isList#(active(X)) -> isList#(X)
p191: U23#(mark(X)) -> U23#(X)
p192: U23#(active(X)) -> U23#(X)
p193: U31#(mark(X1),X2) -> U31#(X1,X2)
p194: U31#(X1,mark(X2)) -> U31#(X1,X2)
p195: U31#(active(X1),X2) -> U31#(X1,X2)
p196: U31#(X1,active(X2)) -> U31#(X1,X2)
p197: U32#(mark(X)) -> U32#(X)
p198: U32#(active(X)) -> U32#(X)
p199: isQid#(mark(X)) -> isQid#(X)
p200: isQid#(active(X)) -> isQid#(X)
p201: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
p202: U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3)
p203: U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3)
p204: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
p205: U41#(X1,active(X2),X3) -> U41#(X1,X2,X3)
p206: U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
p207: U42#(mark(X1),X2) -> U42#(X1,X2)
p208: U42#(X1,mark(X2)) -> U42#(X1,X2)
p209: U42#(active(X1),X2) -> U42#(X1,X2)
p210: U42#(X1,active(X2)) -> U42#(X1,X2)
p211: U43#(mark(X)) -> U43#(X)
p212: U43#(active(X)) -> U43#(X)
p213: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
p214: U51#(X1,mark(X2),X3) -> U51#(X1,X2,X3)
p215: U51#(X1,X2,mark(X3)) -> U51#(X1,X2,X3)
p216: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
p217: U51#(X1,active(X2),X3) -> U51#(X1,X2,X3)
p218: U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
p219: U52#(mark(X1),X2) -> U52#(X1,X2)
p220: U52#(X1,mark(X2)) -> U52#(X1,X2)
p221: U52#(active(X1),X2) -> U52#(X1,X2)
p222: U52#(X1,active(X2)) -> U52#(X1,X2)
p223: U53#(mark(X)) -> U53#(X)
p224: U53#(active(X)) -> U53#(X)
p225: U61#(mark(X1),X2) -> U61#(X1,X2)
p226: U61#(X1,mark(X2)) -> U61#(X1,X2)
p227: U61#(active(X1),X2) -> U61#(X1,X2)
p228: U61#(X1,active(X2)) -> U61#(X1,X2)
p229: U62#(mark(X)) -> U62#(X)
p230: U62#(active(X)) -> U62#(X)
p231: U71#(mark(X1),X2) -> U71#(X1,X2)
p232: U71#(X1,mark(X2)) -> U71#(X1,X2)
p233: U71#(active(X1),X2) -> U71#(X1,X2)
p234: U71#(X1,active(X2)) -> U71#(X1,X2)
p235: U72#(mark(X)) -> U72#(X)
p236: U72#(active(X)) -> U72#(X)
p237: isNePal#(mark(X)) -> isNePal#(X)
p238: isNePal#(active(X)) -> isNePal#(X)
p239: and#(mark(X1),X2) -> and#(X1,X2)
p240: and#(X1,mark(X2)) -> and#(X1,X2)
p241: and#(active(X1),X2) -> and#(X1,X2)
p242: and#(X1,active(X2)) -> and#(X1,X2)
p243: isPalListKind#(mark(X)) -> isPalListKind#(X)
p244: isPalListKind#(active(X)) -> isPalListKind#(X)
p245: isPal#(mark(X)) -> isPal#(X)
p246: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The estimated dependency graph contains the following SCCs:

  {p1, p4, p5, p6, p10, p13, p17, p21, p24, p28, p31, p35, p39, p43, p44, p48, p53, p56, p61, p66, p69, p77, p87, p96, p98, p99, p101, p103, p105, p107, p108, p109, p111, p112, p114, p115, p116, p118, p119, p121, p122, p124, p125, p126, p128, p129, p131, p132, p134, p135, p137, p138, p140, p141, p143, p144, p146, p147, p149, p150, p152, p153, p155, p156, p157, p159, p160, p161}
  {p167, p168, p169, p170}
  {p175, p176}
  {p177, p178}
  {p185, p186, p187, p188}
  {p189, p190}
  {p191, p192}
  {p197, p198}
  {p199, p200}
  {p207, p208, p209, p210}
  {p211, p212}
  {p219, p220, p221, p222}
  {p223, p224}
  {p229, p230}
  {p235, p236}
  {p237, p238}
  {p171, p172, p173, p174}
  {p243, p244}
  {p179, p180, p181, p182, p183, p184}
  {p239, p240, p241, p242}
  {p193, p194, p195, p196}
  {p201, p202, p203, p204, p205, p206}
  {p213, p214, p215, p216, p217, p218}
  {p225, p226, p227, p228}
  {p245, p246}
  {p231, p232, p233, p234}


-- Reduction pair.

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

p1: active#(__(__(X,Y),Z)) -> mark#(__(X,__(Y,Z)))
p2: mark#(isPal(X)) -> active#(isPal(X))
p3: active#(isPalListKind(__(V1,V2))) -> mark#(and(isPalListKind(V1),isPalListKind(V2)))
p4: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p5: active#(isPal(V)) -> mark#(U71(isPalListKind(V),V))
p6: mark#(and(X1,X2)) -> mark#(X1)
p7: mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
p8: active#(isNePal(__(I,__(P,I)))) -> mark#(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
p9: mark#(isNePal(X)) -> active#(isNePal(X))
p10: active#(isNePal(V)) -> mark#(U61(isPalListKind(V),V))
p11: mark#(U72(X)) -> mark#(X)
p12: mark#(U72(X)) -> active#(U72(mark(X)))
p13: active#(isNeList(__(V1,V2))) -> mark#(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
p14: mark#(U71(X1,X2)) -> mark#(X1)
p15: mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
p16: active#(isNeList(__(V1,V2))) -> mark#(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
p17: mark#(U62(X)) -> mark#(X)
p18: mark#(U62(X)) -> active#(U62(mark(X)))
p19: active#(isNeList(V)) -> mark#(U31(isPalListKind(V),V))
p20: mark#(U61(X1,X2)) -> mark#(X1)
p21: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p22: active#(isList(__(V1,V2))) -> mark#(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
p23: mark#(U53(X)) -> mark#(X)
p24: mark#(U53(X)) -> active#(U53(mark(X)))
p25: active#(isList(V)) -> mark#(U11(isPalListKind(V),V))
p26: mark#(U52(X1,X2)) -> mark#(X1)
p27: mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2))
p28: active#(and(tt(),X)) -> mark#(X)
p29: mark#(U51(X1,X2,X3)) -> mark#(X1)
p30: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p31: active#(U71(tt(),V)) -> mark#(U72(isNePal(V)))
p32: mark#(U43(X)) -> mark#(X)
p33: mark#(U43(X)) -> active#(U43(mark(X)))
p34: active#(U61(tt(),V)) -> mark#(U62(isQid(V)))
p35: mark#(U42(X1,X2)) -> mark#(X1)
p36: mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2))
p37: active#(U52(tt(),V2)) -> mark#(U53(isList(V2)))
p38: mark#(U41(X1,X2,X3)) -> mark#(X1)
p39: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p40: active#(U51(tt(),V1,V2)) -> mark#(U52(isNeList(V1),V2))
p41: mark#(isQid(X)) -> active#(isQid(X))
p42: active#(U42(tt(),V2)) -> mark#(U43(isNeList(V2)))
p43: mark#(U32(X)) -> mark#(X)
p44: mark#(U32(X)) -> active#(U32(mark(X)))
p45: active#(U41(tt(),V1,V2)) -> mark#(U42(isList(V1),V2))
p46: mark#(U31(X1,X2)) -> mark#(X1)
p47: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p48: active#(U31(tt(),V)) -> mark#(U32(isQid(V)))
p49: mark#(U23(X)) -> mark#(X)
p50: mark#(U23(X)) -> active#(U23(mark(X)))
p51: active#(U22(tt(),V2)) -> mark#(U23(isList(V2)))
p52: mark#(isList(X)) -> active#(isList(X))
p53: active#(U21(tt(),V1,V2)) -> mark#(U22(isList(V1),V2))
p54: mark#(U22(X1,X2)) -> mark#(X1)
p55: mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
p56: active#(U11(tt(),V)) -> mark#(U12(isNeList(V)))
p57: mark#(U21(X1,X2,X3)) -> mark#(X1)
p58: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p59: active#(__(nil(),X)) -> mark#(X)
p60: mark#(isNeList(X)) -> active#(isNeList(X))
p61: active#(__(X,nil())) -> mark#(X)
p62: mark#(U12(X)) -> mark#(X)
p63: mark#(U12(X)) -> active#(U12(mark(X)))
p64: mark#(U11(X1,X2)) -> mark#(X1)
p65: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p66: mark#(__(X1,X2)) -> mark#(X2)
p67: mark#(__(X1,X2)) -> mark#(X1)
p68: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      u > o > i > e > nil > U12 > __ > U51 > U52 > U53 > U21 > a > U22 > U32 > mark# > U41 > isList > U42 > U11 > isNeList > U43 > tt > isPal > and > U71 > isNePal > isPalListKind > U72 > U61 > U62 > mark > isQid > U31 > active > active# > U23
    
    argument filter:
  
      pi(active#) = 1
      pi(__) = [1, 2]
      pi(mark#) = 1
      pi(isPal) = [1]
      pi(isPalListKind) = 1
      pi(and) = [1, 2]
      pi(U71) = [1, 2]
      pi(mark) = 1
      pi(isNePal) = [1]
      pi(isQid) = 1
      pi(U61) = [1, 2]
      pi(U72) = [1]
      pi(isNeList) = [1]
      pi(U51) = [1, 2, 3]
      pi(U41) = [1, 2, 3]
      pi(U62) = [1]
      pi(U31) = [1, 2]
      pi(isList) = [1]
      pi(U21) = [1, 2, 3]
      pi(U53) = [1]
      pi(U11) = [1, 2]
      pi(U52) = [1, 2]
      pi(tt) = []
      pi(U43) = 1
      pi(U42) = [1, 2]
      pi(U32) = 1
      pi(U23) = 1
      pi(U22) = [1, 2]
      pi(U12) = 1
      pi(nil) = []
      pi(active) = 1
      pi(a) = []
      pi(e) = []
      pi(i) = []
      pi(o) = []
      pi(u) = []

The next rules are strictly ordered:

  p1, p3, p5, p6, p8, p10, p11, p13, p14, p16, p17, p19, p20, p22, p23, p25, p26, p28, p29, p31, p34, p35, p37, p38, p40, p42, p45, p46, p48, p51, p53, p54, p56, p57, p59, p61, p64, p66, p67
  r1, r2, r3, r4, r6, r7, r9, r11, r12, 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

We remove them from the problem.

-- SCC decomposition.

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

p1: mark#(isPal(X)) -> active#(isPal(X))
p2: mark#(isPalListKind(X)) -> active#(isPalListKind(X))
p3: mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
p4: mark#(isNePal(X)) -> active#(isNePal(X))
p5: mark#(U72(X)) -> active#(U72(mark(X)))
p6: mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2))
p7: mark#(U62(X)) -> active#(U62(mark(X)))
p8: mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2))
p9: mark#(U53(X)) -> active#(U53(mark(X)))
p10: mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2))
p11: mark#(U51(X1,X2,X3)) -> active#(U51(mark(X1),X2,X3))
p12: mark#(U43(X)) -> mark#(X)
p13: mark#(U43(X)) -> active#(U43(mark(X)))
p14: mark#(U42(X1,X2)) -> active#(U42(mark(X1),X2))
p15: mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3))
p16: mark#(isQid(X)) -> active#(isQid(X))
p17: mark#(U32(X)) -> mark#(X)
p18: mark#(U32(X)) -> active#(U32(mark(X)))
p19: mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2))
p20: mark#(U23(X)) -> mark#(X)
p21: mark#(U23(X)) -> active#(U23(mark(X)))
p22: mark#(isList(X)) -> active#(isList(X))
p23: mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2))
p24: mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
p25: mark#(isNeList(X)) -> active#(isNeList(X))
p26: mark#(U12(X)) -> mark#(X)
p27: mark#(U12(X)) -> active#(U12(mark(X)))
p28: mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
p29: mark#(__(X1,X2)) -> active#(__(mark(X1),mark(X2)))

and R consists of:

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

The estimated dependency graph contains the following SCCs:

  {p12, p17, p20, p26}


-- Reduction pair.

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

p1: mark#(U43(X)) -> mark#(X)
p2: mark#(U12(X)) -> mark#(X)
p3: mark#(U23(X)) -> mark#(X)
p4: mark#(U32(X)) -> mark#(X)

and R consists of:

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

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      mark# > U32 > U23 > U12 > U43
    
    argument filter:
  
      pi(mark#) = 1
      pi(U43) = [1]
      pi(U12) = [1]
      pi(U23) = [1]
      pi(U32) = [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

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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: __#(mark(X1),X2) -> __#(X1,X2)
p2: __#(active(X1),X2) -> __#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      __# > active > mark
    
    argument filter:
  
      pi(__#) = 1
      pi(mark) = [1]
      pi(active) = [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: U12#(mark(X)) -> U12#(X)
p2: U12#(active(X)) -> U12#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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) -> U22#(X1,X2)
p2: U22#(X1,active(X2)) -> U22#(X1,X2)
p3: U22#(active(X1),X2) -> U22#(X1,X2)
p4: U22#(X1,mark(X2)) -> U22#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U22# > active > mark
    
    argument filter:
  
      pi(U22#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

p1: U22#(mark(X1),X2) -> U22#(X1,X2)
p2: U22#(active(X1),X2) -> U22#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U22#(mark(X1),X2) -> U22#(X1,X2)
p2: U22#(active(X1),X2) -> U22#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U22# > active > mark
    
    argument filter:
  
      pi(U22#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(X)) -> U23#(X)
p2: U23#(active(X)) -> U23#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(X)) -> U32#(X)
p2: U32#(active(X)) -> U32#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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) -> U42#(X1,X2)
p2: U42#(X1,active(X2)) -> U42#(X1,X2)
p3: U42#(active(X1),X2) -> U42#(X1,X2)
p4: U42#(X1,mark(X2)) -> U42#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U42# > active > mark
    
    argument filter:
  
      pi(U42#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

p1: U42#(mark(X1),X2) -> U42#(X1,X2)
p2: U42#(active(X1),X2) -> U42#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U42#(mark(X1),X2) -> U42#(X1,X2)
p2: U42#(active(X1),X2) -> U42#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U42# > active > mark
    
    argument filter:
  
      pi(U42#) = 1
      pi(mark) = [1]
      pi(active) = [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: U43#(mark(X)) -> U43#(X)
p2: U43#(active(X)) -> U43#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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) -> U52#(X1,X2)
p2: U52#(X1,active(X2)) -> U52#(X1,X2)
p3: U52#(active(X1),X2) -> U52#(X1,X2)
p4: U52#(X1,mark(X2)) -> U52#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U52# > active > mark
    
    argument filter:
  
      pi(U52#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

p1: U52#(mark(X1),X2) -> U52#(X1,X2)
p2: U52#(active(X1),X2) -> U52#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U52#(mark(X1),X2) -> U52#(X1,X2)
p2: U52#(active(X1),X2) -> U52#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U52# > active > mark
    
    argument filter:
  
      pi(U52#) = 1
      pi(mark) = [1]
      pi(active) = [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: U53#(mark(X)) -> U53#(X)
p2: U53#(active(X)) -> U53#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(X)) -> U62#(X)
p2: U62#(active(X)) -> U62#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(X)) -> U72#(X)
p2: U72#(active(X)) -> U72#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U11#(mark(X1),X2) -> U11#(X1,X2)
p2: U11#(active(X1),X2) -> U11#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U11# > active > mark
    
    argument filter:
  
      pi(U11#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U21# > active > mark
    
    argument filter:
  
      pi(U21#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p3, p6

We remove them from the problem.

-- SCC decomposition.

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

p1: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
p2: U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
p3: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
p4: U21#(X1,X2,mark(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4}


-- 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,mark(X3)) -> U21#(X1,X2,X3)
p3: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
p4: U21#(X1,X2,active(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
p2: U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U21# > active > mark
    
    argument filter:
  
      pi(U21#) = 1
      pi(mark) = [1]
      pi(active) = [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: and#(mark(X1),X2) -> and#(X1,X2)
p2: and#(X1,active(X2)) -> and#(X1,X2)
p3: and#(active(X1),X2) -> and#(X1,X2)
p4: and#(X1,mark(X2)) -> and#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

p1: and#(mark(X1),X2) -> and#(X1,X2)
p2: and#(active(X1),X2) -> and#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: and#(mark(X1),X2) -> and#(X1,X2)
p2: and#(active(X1),X2) -> and#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      and# > active > mark
    
    argument filter:
  
      pi(and#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U31#(mark(X1),X2) -> U31#(X1,X2)
p2: U31#(active(X1),X2) -> U31#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U31# > active > mark
    
    argument filter:
  
      pi(U31#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U41# > active > mark
    
    argument filter:
  
      pi(U41#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p3, p6

We remove them from the problem.

-- SCC decomposition.

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

p1: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
p2: U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3)
p3: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
p4: U41#(X1,X2,mark(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4}


-- 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,mark(X3)) -> U41#(X1,X2,X3)
p3: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)
p4: U41#(X1,X2,active(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3)
p2: U41#(active(X1),X2,X3) -> U41#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U41# > active > mark
    
    argument filter:
  
      pi(U41#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U51# > active > mark
    
    argument filter:
  
      pi(U51#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p3, p6

We remove them from the problem.

-- SCC decomposition.

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

p1: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
p2: U51#(X1,X2,active(X3)) -> U51#(X1,X2,X3)
p3: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
p4: U51#(X1,X2,mark(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4}


-- 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,mark(X3)) -> U51#(X1,X2,X3)
p3: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)
p4: U51#(X1,X2,active(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U51#(mark(X1),X2,X3) -> U51#(X1,X2,X3)
p2: U51#(active(X1),X2,X3) -> U51#(X1,X2,X3)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U51# > active > mark
    
    argument filter:
  
      pi(U51#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

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

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U61#(mark(X1),X2) -> U61#(X1,X2)
p2: U61#(active(X1),X2) -> U61#(X1,X2)

and R consists of:

r1: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
r2: active(__(X,nil())) -> mark(X)
r3: active(__(nil(),X)) -> mark(X)
r4: active(U11(tt(),V)) -> mark(U12(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U61# > active > mark
    
    argument filter:
  
      pi(U61#) = 1
      pi(mark) = [1]
      pi(active) = [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: 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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the monotone reduction pair:

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

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) -> U71#(X1,X2)
p2: U71#(X1,active(X2)) -> U71#(X1,X2)
p3: U71#(active(X1),X2) -> U71#(X1,X2)
p4: U71#(X1,mark(X2)) -> U71#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

  lexicographic path order with precedence:
  
    precedence:
    
      U71# > active > mark
    
    argument filter:
  
      pi(U71#) = 2
      pi(mark) = [1]
      pi(active) = [1]

The next rules are strictly ordered:

  p2, p4

We remove them from the problem.

-- SCC decomposition.

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

p1: U71#(mark(X1),X2) -> U71#(X1,X2)
p2: U71#(active(X1),X2) -> U71#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(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: U71#(mark(X1),X2) -> U71#(X1,X2)
p2: U71#(active(X1),X2) -> U71#(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(isNeList(V)))
r5: active(U12(tt())) -> mark(tt())
r6: active(U21(tt(),V1,V2)) -> mark(U22(isList(V1),V2))
r7: active(U22(tt(),V2)) -> mark(U23(isList(V2)))
r8: active(U23(tt())) -> mark(tt())
r9: active(U31(tt(),V)) -> mark(U32(isQid(V)))
r10: active(U32(tt())) -> mark(tt())
r11: active(U41(tt(),V1,V2)) -> mark(U42(isList(V1),V2))
r12: active(U42(tt(),V2)) -> mark(U43(isNeList(V2)))
r13: active(U43(tt())) -> mark(tt())
r14: active(U51(tt(),V1,V2)) -> mark(U52(isNeList(V1),V2))
r15: active(U52(tt(),V2)) -> mark(U53(isList(V2)))
r16: active(U53(tt())) -> mark(tt())
r17: active(U61(tt(),V)) -> mark(U62(isQid(V)))
r18: active(U62(tt())) -> mark(tt())
r19: active(U71(tt(),V)) -> mark(U72(isNePal(V)))
r20: active(U72(tt())) -> mark(tt())
r21: active(and(tt(),X)) -> mark(X)
r22: active(isList(V)) -> mark(U11(isPalListKind(V),V))
r23: active(isList(nil())) -> mark(tt())
r24: active(isList(__(V1,V2))) -> mark(U21(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r25: active(isNeList(V)) -> mark(U31(isPalListKind(V),V))
r26: active(isNeList(__(V1,V2))) -> mark(U41(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r27: active(isNeList(__(V1,V2))) -> mark(U51(and(isPalListKind(V1),isPalListKind(V2)),V1,V2))
r28: active(isNePal(V)) -> mark(U61(isPalListKind(V),V))
r29: active(isNePal(__(I,__(P,I)))) -> mark(and(and(isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P))))
r30: active(isPal(V)) -> mark(U71(isPalListKind(V),V))
r31: active(isPal(nil())) -> mark(tt())
r32: active(isPalListKind(a())) -> mark(tt())
r33: active(isPalListKind(e())) -> mark(tt())
r34: active(isPalListKind(i())) -> mark(tt())
r35: active(isPalListKind(nil())) -> mark(tt())
r36: active(isPalListKind(o())) -> mark(tt())
r37: active(isPalListKind(u())) -> mark(tt())
r38: active(isPalListKind(__(V1,V2))) -> mark(and(isPalListKind(V1),isPalListKind(V2)))
r39: active(isQid(a())) -> mark(tt())
r40: active(isQid(e())) -> mark(tt())
r41: active(isQid(i())) -> mark(tt())
r42: active(isQid(o())) -> mark(tt())
r43: active(isQid(u())) -> mark(tt())
r44: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
r45: mark(nil()) -> active(nil())
r46: mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
r47: mark(tt()) -> active(tt())
r48: mark(U12(X)) -> active(U12(mark(X)))
r49: mark(isNeList(X)) -> active(isNeList(X))
r50: mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
r51: mark(U22(X1,X2)) -> active(U22(mark(X1),X2))
r52: mark(isList(X)) -> active(isList(X))
r53: mark(U23(X)) -> active(U23(mark(X)))
r54: mark(U31(X1,X2)) -> active(U31(mark(X1),X2))
r55: mark(U32(X)) -> active(U32(mark(X)))
r56: mark(isQid(X)) -> active(isQid(X))
r57: mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3))
r58: mark(U42(X1,X2)) -> active(U42(mark(X1),X2))
r59: mark(U43(X)) -> active(U43(mark(X)))
r60: mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
r61: mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
r62: mark(U53(X)) -> active(U53(mark(X)))
r63: mark(U61(X1,X2)) -> active(U61(mark(X1),X2))
r64: mark(U62(X)) -> active(U62(mark(X)))
r65: mark(U71(X1,X2)) -> active(U71(mark(X1),X2))
r66: mark(U72(X)) -> active(U72(mark(X)))
r67: mark(isNePal(X)) -> active(isNePal(X))
r68: mark(and(X1,X2)) -> active(and(mark(X1),X2))
r69: mark(isPalListKind(X)) -> active(isPalListKind(X))
r70: mark(isPal(X)) -> active(isPal(X))
r71: mark(a()) -> active(a())
r72: mark(e()) -> active(e())
r73: mark(i()) -> active(i())
r74: mark(o()) -> active(o())
r75: mark(u()) -> active(u())
r76: __(mark(X1),X2) -> __(X1,X2)
r77: __(X1,mark(X2)) -> __(X1,X2)
r78: __(active(X1),X2) -> __(X1,X2)
r79: __(X1,active(X2)) -> __(X1,X2)
r80: U11(mark(X1),X2) -> U11(X1,X2)
r81: U11(X1,mark(X2)) -> U11(X1,X2)
r82: U11(active(X1),X2) -> U11(X1,X2)
r83: U11(X1,active(X2)) -> U11(X1,X2)
r84: U12(mark(X)) -> U12(X)
r85: U12(active(X)) -> U12(X)
r86: isNeList(mark(X)) -> isNeList(X)
r87: isNeList(active(X)) -> isNeList(X)
r88: U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
r89: U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
r90: U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
r91: U21(active(X1),X2,X3) -> U21(X1,X2,X3)
r92: U21(X1,active(X2),X3) -> U21(X1,X2,X3)
r93: U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
r94: U22(mark(X1),X2) -> U22(X1,X2)
r95: U22(X1,mark(X2)) -> U22(X1,X2)
r96: U22(active(X1),X2) -> U22(X1,X2)
r97: U22(X1,active(X2)) -> U22(X1,X2)
r98: isList(mark(X)) -> isList(X)
r99: isList(active(X)) -> isList(X)
r100: U23(mark(X)) -> U23(X)
r101: U23(active(X)) -> U23(X)
r102: U31(mark(X1),X2) -> U31(X1,X2)
r103: U31(X1,mark(X2)) -> U31(X1,X2)
r104: U31(active(X1),X2) -> U31(X1,X2)
r105: U31(X1,active(X2)) -> U31(X1,X2)
r106: U32(mark(X)) -> U32(X)
r107: U32(active(X)) -> U32(X)
r108: isQid(mark(X)) -> isQid(X)
r109: isQid(active(X)) -> isQid(X)
r110: U41(mark(X1),X2,X3) -> U41(X1,X2,X3)
r111: U41(X1,mark(X2),X3) -> U41(X1,X2,X3)
r112: U41(X1,X2,mark(X3)) -> U41(X1,X2,X3)
r113: U41(active(X1),X2,X3) -> U41(X1,X2,X3)
r114: U41(X1,active(X2),X3) -> U41(X1,X2,X3)
r115: U41(X1,X2,active(X3)) -> U41(X1,X2,X3)
r116: U42(mark(X1),X2) -> U42(X1,X2)
r117: U42(X1,mark(X2)) -> U42(X1,X2)
r118: U42(active(X1),X2) -> U42(X1,X2)
r119: U42(X1,active(X2)) -> U42(X1,X2)
r120: U43(mark(X)) -> U43(X)
r121: U43(active(X)) -> U43(X)
r122: U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
r123: U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
r124: U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
r125: U51(active(X1),X2,X3) -> U51(X1,X2,X3)
r126: U51(X1,active(X2),X3) -> U51(X1,X2,X3)
r127: U51(X1,X2,active(X3)) -> U51(X1,X2,X3)
r128: U52(mark(X1),X2) -> U52(X1,X2)
r129: U52(X1,mark(X2)) -> U52(X1,X2)
r130: U52(active(X1),X2) -> U52(X1,X2)
r131: U52(X1,active(X2)) -> U52(X1,X2)
r132: U53(mark(X)) -> U53(X)
r133: U53(active(X)) -> U53(X)
r134: U61(mark(X1),X2) -> U61(X1,X2)
r135: U61(X1,mark(X2)) -> U61(X1,X2)
r136: U61(active(X1),X2) -> U61(X1,X2)
r137: U61(X1,active(X2)) -> U61(X1,X2)
r138: U62(mark(X)) -> U62(X)
r139: U62(active(X)) -> U62(X)
r140: U71(mark(X1),X2) -> U71(X1,X2)
r141: U71(X1,mark(X2)) -> U71(X1,X2)
r142: U71(active(X1),X2) -> U71(X1,X2)
r143: U71(X1,active(X2)) -> U71(X1,X2)
r144: U72(mark(X)) -> U72(X)
r145: U72(active(X)) -> U72(X)
r146: isNePal(mark(X)) -> isNePal(X)
r147: isNePal(active(X)) -> isNePal(X)
r148: and(mark(X1),X2) -> and(X1,X2)
r149: and(X1,mark(X2)) -> and(X1,X2)
r150: and(active(X1),X2) -> and(X1,X2)
r151: and(X1,active(X2)) -> and(X1,X2)
r152: isPalListKind(mark(X)) -> isPalListKind(X)
r153: isPalListKind(active(X)) -> isPalListKind(X)
r154: isPal(mark(X)) -> isPal(X)
r155: isPal(active(X)) -> isPal(X)

The set of usable rules consists of

  (no rules)

Take the reduction pair:

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

The next rules are strictly ordered:

  p1, p2

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