YES

We show the termination of the TRS R:

  a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
  a____(X,nil()) -> mark(X)
  a____(nil(),X) -> mark(X)
  a__U11(tt(),V) -> a__U12(a__isNeList(V))
  a__U12(tt()) -> tt()
  a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2)
  a__U22(tt(),V2) -> a__U23(a__isList(V2))
  a__U23(tt()) -> tt()
  a__U31(tt(),V) -> a__U32(a__isQid(V))
  a__U32(tt()) -> tt()
  a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2)
  a__U42(tt(),V2) -> a__U43(a__isNeList(V2))
  a__U43(tt()) -> tt()
  a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2)
  a__U52(tt(),V2) -> a__U53(a__isList(V2))
  a__U53(tt()) -> tt()
  a__U61(tt(),V) -> a__U62(a__isQid(V))
  a__U62(tt()) -> tt()
  a__U71(tt(),V) -> a__U72(a__isNePal(V))
  a__U72(tt()) -> tt()
  a__and(tt(),X) -> mark(X)
  a__isList(V) -> a__U11(a__isPalListKind(V),V)
  a__isList(nil()) -> tt()
  a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
  a__isNeList(V) -> a__U31(a__isPalListKind(V),V)
  a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
  a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
  a__isNePal(V) -> a__U61(a__isPalListKind(V),V)
  a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
  a__isPal(V) -> a__U71(a__isPalListKind(V),V)
  a__isPal(nil()) -> tt()
  a__isPalListKind(a()) -> tt()
  a__isPalListKind(e()) -> tt()
  a__isPalListKind(i()) -> tt()
  a__isPalListKind(nil()) -> tt()
  a__isPalListKind(o()) -> tt()
  a__isPalListKind(u()) -> tt()
  a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2))
  a__isQid(a()) -> tt()
  a__isQid(e()) -> tt()
  a__isQid(i()) -> tt()
  a__isQid(o()) -> tt()
  a__isQid(u()) -> tt()
  mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
  mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
  mark(U12(X)) -> a__U12(mark(X))
  mark(isNeList(X)) -> a__isNeList(X)
  mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
  mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
  mark(isList(X)) -> a__isList(X)
  mark(U23(X)) -> a__U23(mark(X))
  mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
  mark(U32(X)) -> a__U32(mark(X))
  mark(isQid(X)) -> a__isQid(X)
  mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
  mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
  mark(U43(X)) -> a__U43(mark(X))
  mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
  mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
  mark(U53(X)) -> a__U53(mark(X))
  mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
  mark(U62(X)) -> a__U62(mark(X))
  mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
  mark(U72(X)) -> a__U72(mark(X))
  mark(isNePal(X)) -> a__isNePal(X)
  mark(and(X1,X2)) -> a__and(mark(X1),X2)
  mark(isPalListKind(X)) -> a__isPalListKind(X)
  mark(isPal(X)) -> a__isPal(X)
  mark(nil()) -> nil()
  mark(tt()) -> tt()
  mark(a()) -> a()
  mark(e()) -> e()
  mark(i()) -> i()
  mark(o()) -> o()
  mark(u()) -> u()
  a____(X1,X2) -> __(X1,X2)
  a__U11(X1,X2) -> U11(X1,X2)
  a__U12(X) -> U12(X)
  a__isNeList(X) -> isNeList(X)
  a__U21(X1,X2,X3) -> U21(X1,X2,X3)
  a__U22(X1,X2) -> U22(X1,X2)
  a__isList(X) -> isList(X)
  a__U23(X) -> U23(X)
  a__U31(X1,X2) -> U31(X1,X2)
  a__U32(X) -> U32(X)
  a__isQid(X) -> isQid(X)
  a__U41(X1,X2,X3) -> U41(X1,X2,X3)
  a__U42(X1,X2) -> U42(X1,X2)
  a__U43(X) -> U43(X)
  a__U51(X1,X2,X3) -> U51(X1,X2,X3)
  a__U52(X1,X2) -> U52(X1,X2)
  a__U53(X) -> U53(X)
  a__U61(X1,X2) -> U61(X1,X2)
  a__U62(X) -> U62(X)
  a__U71(X1,X2) -> U71(X1,X2)
  a__U72(X) -> U72(X)
  a__isNePal(X) -> isNePal(X)
  a__and(X1,X2) -> and(X1,X2)
  a__isPalListKind(X) -> isPalListKind(X)
  a__isPal(X) -> isPal(X)

-- SCC decomposition.

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

p1: a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
p2: a____#(__(X,Y),Z) -> mark#(X)
p3: a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
p4: a____#(__(X,Y),Z) -> mark#(Y)
p5: a____#(__(X,Y),Z) -> mark#(Z)
p6: a____#(X,nil()) -> mark#(X)
p7: a____#(nil(),X) -> mark#(X)
p8: a__U11#(tt(),V) -> a__U12#(a__isNeList(V))
p9: a__U11#(tt(),V) -> a__isNeList#(V)
p10: a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2)
p11: a__U21#(tt(),V1,V2) -> a__isList#(V1)
p12: a__U22#(tt(),V2) -> a__U23#(a__isList(V2))
p13: a__U22#(tt(),V2) -> a__isList#(V2)
p14: a__U31#(tt(),V) -> a__U32#(a__isQid(V))
p15: a__U31#(tt(),V) -> a__isQid#(V)
p16: a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2)
p17: a__U41#(tt(),V1,V2) -> a__isList#(V1)
p18: a__U42#(tt(),V2) -> a__U43#(a__isNeList(V2))
p19: a__U42#(tt(),V2) -> a__isNeList#(V2)
p20: a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2)
p21: a__U51#(tt(),V1,V2) -> a__isNeList#(V1)
p22: a__U52#(tt(),V2) -> a__U53#(a__isList(V2))
p23: a__U52#(tt(),V2) -> a__isList#(V2)
p24: a__U61#(tt(),V) -> a__U62#(a__isQid(V))
p25: a__U61#(tt(),V) -> a__isQid#(V)
p26: a__U71#(tt(),V) -> a__U72#(a__isNePal(V))
p27: a__U71#(tt(),V) -> a__isNePal#(V)
p28: a__and#(tt(),X) -> mark#(X)
p29: a__isList#(V) -> a__U11#(a__isPalListKind(V),V)
p30: a__isList#(V) -> a__isPalListKind#(V)
p31: a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
p32: a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p33: a__isList#(__(V1,V2)) -> a__isPalListKind#(V1)
p34: a__isNeList#(V) -> a__U31#(a__isPalListKind(V),V)
p35: a__isNeList#(V) -> a__isPalListKind#(V)
p36: a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
p37: a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p38: a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1)
p39: a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
p40: a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p41: a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1)
p42: a__isNePal#(V) -> a__U61#(a__isPalListKind(V),V)
p43: a__isNePal#(V) -> a__isPalListKind#(V)
p44: a__isNePal#(__(I,__(P,I))) -> a__and#(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
p45: a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPalListKind(I))
p46: a__isNePal#(__(I,__(P,I))) -> a__isQid#(I)
p47: a__isPal#(V) -> a__U71#(a__isPalListKind(V),V)
p48: a__isPal#(V) -> a__isPalListKind#(V)
p49: a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p50: a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1)
p51: mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
p52: mark#(__(X1,X2)) -> mark#(X1)
p53: mark#(__(X1,X2)) -> mark#(X2)
p54: mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
p55: mark#(U11(X1,X2)) -> mark#(X1)
p56: mark#(U12(X)) -> a__U12#(mark(X))
p57: mark#(U12(X)) -> mark#(X)
p58: mark#(isNeList(X)) -> a__isNeList#(X)
p59: mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3)
p60: mark#(U21(X1,X2,X3)) -> mark#(X1)
p61: mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2)
p62: mark#(U22(X1,X2)) -> mark#(X1)
p63: mark#(isList(X)) -> a__isList#(X)
p64: mark#(U23(X)) -> a__U23#(mark(X))
p65: mark#(U23(X)) -> mark#(X)
p66: mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2)
p67: mark#(U31(X1,X2)) -> mark#(X1)
p68: mark#(U32(X)) -> a__U32#(mark(X))
p69: mark#(U32(X)) -> mark#(X)
p70: mark#(isQid(X)) -> a__isQid#(X)
p71: mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3)
p72: mark#(U41(X1,X2,X3)) -> mark#(X1)
p73: mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2)
p74: mark#(U42(X1,X2)) -> mark#(X1)
p75: mark#(U43(X)) -> a__U43#(mark(X))
p76: mark#(U43(X)) -> mark#(X)
p77: mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3)
p78: mark#(U51(X1,X2,X3)) -> mark#(X1)
p79: mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2)
p80: mark#(U52(X1,X2)) -> mark#(X1)
p81: mark#(U53(X)) -> a__U53#(mark(X))
p82: mark#(U53(X)) -> mark#(X)
p83: mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2)
p84: mark#(U61(X1,X2)) -> mark#(X1)
p85: mark#(U62(X)) -> a__U62#(mark(X))
p86: mark#(U62(X)) -> mark#(X)
p87: mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2)
p88: mark#(U71(X1,X2)) -> mark#(X1)
p89: mark#(U72(X)) -> a__U72#(mark(X))
p90: mark#(U72(X)) -> mark#(X)
p91: mark#(isNePal(X)) -> a__isNePal#(X)
p92: mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
p93: mark#(and(X1,X2)) -> mark#(X1)
p94: mark#(isPalListKind(X)) -> a__isPalListKind#(X)
p95: mark#(isPal(X)) -> a__isPal#(X)

and R consists of:

r1: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
r2: a____(X,nil()) -> mark(X)
r3: a____(nil(),X) -> mark(X)
r4: a__U11(tt(),V) -> a__U12(a__isNeList(V))
r5: a__U12(tt()) -> tt()
r6: a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2)
r7: a__U22(tt(),V2) -> a__U23(a__isList(V2))
r8: a__U23(tt()) -> tt()
r9: a__U31(tt(),V) -> a__U32(a__isQid(V))
r10: a__U32(tt()) -> tt()
r11: a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2)
r12: a__U42(tt(),V2) -> a__U43(a__isNeList(V2))
r13: a__U43(tt()) -> tt()
r14: a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2)
r15: a__U52(tt(),V2) -> a__U53(a__isList(V2))
r16: a__U53(tt()) -> tt()
r17: a__U61(tt(),V) -> a__U62(a__isQid(V))
r18: a__U62(tt()) -> tt()
r19: a__U71(tt(),V) -> a__U72(a__isNePal(V))
r20: a__U72(tt()) -> tt()
r21: a__and(tt(),X) -> mark(X)
r22: a__isList(V) -> a__U11(a__isPalListKind(V),V)
r23: a__isList(nil()) -> tt()
r24: a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r25: a__isNeList(V) -> a__U31(a__isPalListKind(V),V)
r26: a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r27: a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r28: a__isNePal(V) -> a__U61(a__isPalListKind(V),V)
r29: a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
r30: a__isPal(V) -> a__U71(a__isPalListKind(V),V)
r31: a__isPal(nil()) -> tt()
r32: a__isPalListKind(a()) -> tt()
r33: a__isPalListKind(e()) -> tt()
r34: a__isPalListKind(i()) -> tt()
r35: a__isPalListKind(nil()) -> tt()
r36: a__isPalListKind(o()) -> tt()
r37: a__isPalListKind(u()) -> tt()
r38: a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2))
r39: a__isQid(a()) -> tt()
r40: a__isQid(e()) -> tt()
r41: a__isQid(i()) -> tt()
r42: a__isQid(o()) -> tt()
r43: a__isQid(u()) -> tt()
r44: mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
r45: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
r46: mark(U12(X)) -> a__U12(mark(X))
r47: mark(isNeList(X)) -> a__isNeList(X)
r48: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
r49: mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
r50: mark(isList(X)) -> a__isList(X)
r51: mark(U23(X)) -> a__U23(mark(X))
r52: mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
r53: mark(U32(X)) -> a__U32(mark(X))
r54: mark(isQid(X)) -> a__isQid(X)
r55: mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
r56: mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
r57: mark(U43(X)) -> a__U43(mark(X))
r58: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
r59: mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
r60: mark(U53(X)) -> a__U53(mark(X))
r61: mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
r62: mark(U62(X)) -> a__U62(mark(X))
r63: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
r64: mark(U72(X)) -> a__U72(mark(X))
r65: mark(isNePal(X)) -> a__isNePal(X)
r66: mark(and(X1,X2)) -> a__and(mark(X1),X2)
r67: mark(isPalListKind(X)) -> a__isPalListKind(X)
r68: mark(isPal(X)) -> a__isPal(X)
r69: mark(nil()) -> nil()
r70: mark(tt()) -> tt()
r71: mark(a()) -> a()
r72: mark(e()) -> e()
r73: mark(i()) -> i()
r74: mark(o()) -> o()
r75: mark(u()) -> u()
r76: a____(X1,X2) -> __(X1,X2)
r77: a__U11(X1,X2) -> U11(X1,X2)
r78: a__U12(X) -> U12(X)
r79: a__isNeList(X) -> isNeList(X)
r80: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
r81: a__U22(X1,X2) -> U22(X1,X2)
r82: a__isList(X) -> isList(X)
r83: a__U23(X) -> U23(X)
r84: a__U31(X1,X2) -> U31(X1,X2)
r85: a__U32(X) -> U32(X)
r86: a__isQid(X) -> isQid(X)
r87: a__U41(X1,X2,X3) -> U41(X1,X2,X3)
r88: a__U42(X1,X2) -> U42(X1,X2)
r89: a__U43(X) -> U43(X)
r90: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
r91: a__U52(X1,X2) -> U52(X1,X2)
r92: a__U53(X) -> U53(X)
r93: a__U61(X1,X2) -> U61(X1,X2)
r94: a__U62(X) -> U62(X)
r95: a__U71(X1,X2) -> U71(X1,X2)
r96: a__U72(X) -> U72(X)
r97: a__isNePal(X) -> isNePal(X)
r98: a__and(X1,X2) -> and(X1,X2)
r99: a__isPalListKind(X) -> isPalListKind(X)
r100: a__isPal(X) -> isPal(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4, p5, p6, p7, p9, p10, p11, p13, p16, p17, p19, p20, p21, p23, p27, p28, p29, p30, p31, p32, p33, p35, p36, p37, p38, p39, p40, p41, p43, p44, p45, p47, p48, p49, p50, p51, p52, p53, p54, p55, p57, p58, p59, p60, p61, p62, p63, p65, p67, p69, p71, p72, p73, p74, p76, p77, p78, p79, p80, p82, p84, p86, p87, p88, p90, p91, p92, p93, p94, p95}


-- Reduction pair.

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

p1: a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
p2: a____#(nil(),X) -> mark#(X)
p3: mark#(isPal(X)) -> a__isPal#(X)
p4: a__isPal#(V) -> a__isPalListKind#(V)
p5: a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1)
p6: a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p7: a__and#(tt(),X) -> mark#(X)
p8: mark#(isPalListKind(X)) -> a__isPalListKind#(X)
p9: mark#(and(X1,X2)) -> mark#(X1)
p10: mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
p11: mark#(isNePal(X)) -> a__isNePal#(X)
p12: a__isNePal#(__(I,__(P,I))) -> a__and#(a__isQid(I),isPalListKind(I))
p13: a__isNePal#(__(I,__(P,I))) -> a__and#(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
p14: a__isNePal#(V) -> a__isPalListKind#(V)
p15: mark#(U72(X)) -> mark#(X)
p16: mark#(U71(X1,X2)) -> mark#(X1)
p17: mark#(U71(X1,X2)) -> a__U71#(mark(X1),X2)
p18: a__U71#(tt(),V) -> a__isNePal#(V)
p19: mark#(U62(X)) -> mark#(X)
p20: mark#(U61(X1,X2)) -> mark#(X1)
p21: mark#(U53(X)) -> mark#(X)
p22: mark#(U52(X1,X2)) -> mark#(X1)
p23: mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2)
p24: a__U52#(tt(),V2) -> a__isList#(V2)
p25: a__isList#(__(V1,V2)) -> a__isPalListKind#(V1)
p26: a__isList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p27: a__isList#(__(V1,V2)) -> a__U21#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
p28: a__U21#(tt(),V1,V2) -> a__isList#(V1)
p29: a__isList#(V) -> a__isPalListKind#(V)
p30: a__isList#(V) -> a__U11#(a__isPalListKind(V),V)
p31: a__U11#(tt(),V) -> a__isNeList#(V)
p32: a__isNeList#(__(V1,V2)) -> a__isPalListKind#(V1)
p33: a__isNeList#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p34: a__isNeList#(__(V1,V2)) -> a__U51#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
p35: a__U51#(tt(),V1,V2) -> a__isNeList#(V1)
p36: a__isNeList#(__(V1,V2)) -> a__U41#(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
p37: a__U41#(tt(),V1,V2) -> a__isList#(V1)
p38: a__U41#(tt(),V1,V2) -> a__U42#(a__isList(V1),V2)
p39: a__U42#(tt(),V2) -> a__isNeList#(V2)
p40: a__isNeList#(V) -> a__isPalListKind#(V)
p41: a__U51#(tt(),V1,V2) -> a__U52#(a__isNeList(V1),V2)
p42: a__U21#(tt(),V1,V2) -> a__U22#(a__isList(V1),V2)
p43: a__U22#(tt(),V2) -> a__isList#(V2)
p44: mark#(U51(X1,X2,X3)) -> mark#(X1)
p45: mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3)
p46: mark#(U43(X)) -> mark#(X)
p47: mark#(U42(X1,X2)) -> mark#(X1)
p48: mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2)
p49: mark#(U41(X1,X2,X3)) -> mark#(X1)
p50: mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3)
p51: mark#(U32(X)) -> mark#(X)
p52: mark#(U31(X1,X2)) -> mark#(X1)
p53: mark#(U23(X)) -> mark#(X)
p54: mark#(isList(X)) -> a__isList#(X)
p55: mark#(U22(X1,X2)) -> mark#(X1)
p56: mark#(U22(X1,X2)) -> a__U22#(mark(X1),X2)
p57: mark#(U21(X1,X2,X3)) -> mark#(X1)
p58: mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3)
p59: mark#(isNeList(X)) -> a__isNeList#(X)
p60: mark#(U12(X)) -> mark#(X)
p61: mark#(U11(X1,X2)) -> mark#(X1)
p62: mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2)
p63: mark#(__(X1,X2)) -> mark#(X2)
p64: mark#(__(X1,X2)) -> mark#(X1)
p65: mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
p66: a____#(X,nil()) -> mark#(X)
p67: a____#(__(X,Y),Z) -> mark#(Z)
p68: a____#(__(X,Y),Z) -> mark#(Y)
p69: a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
p70: a____#(__(X,Y),Z) -> mark#(X)
p71: a__isPal#(V) -> a__U71#(a__isPalListKind(V),V)

and R consists of:

r1: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
r2: a____(X,nil()) -> mark(X)
r3: a____(nil(),X) -> mark(X)
r4: a__U11(tt(),V) -> a__U12(a__isNeList(V))
r5: a__U12(tt()) -> tt()
r6: a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2)
r7: a__U22(tt(),V2) -> a__U23(a__isList(V2))
r8: a__U23(tt()) -> tt()
r9: a__U31(tt(),V) -> a__U32(a__isQid(V))
r10: a__U32(tt()) -> tt()
r11: a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2)
r12: a__U42(tt(),V2) -> a__U43(a__isNeList(V2))
r13: a__U43(tt()) -> tt()
r14: a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2)
r15: a__U52(tt(),V2) -> a__U53(a__isList(V2))
r16: a__U53(tt()) -> tt()
r17: a__U61(tt(),V) -> a__U62(a__isQid(V))
r18: a__U62(tt()) -> tt()
r19: a__U71(tt(),V) -> a__U72(a__isNePal(V))
r20: a__U72(tt()) -> tt()
r21: a__and(tt(),X) -> mark(X)
r22: a__isList(V) -> a__U11(a__isPalListKind(V),V)
r23: a__isList(nil()) -> tt()
r24: a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r25: a__isNeList(V) -> a__U31(a__isPalListKind(V),V)
r26: a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r27: a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r28: a__isNePal(V) -> a__U61(a__isPalListKind(V),V)
r29: a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
r30: a__isPal(V) -> a__U71(a__isPalListKind(V),V)
r31: a__isPal(nil()) -> tt()
r32: a__isPalListKind(a()) -> tt()
r33: a__isPalListKind(e()) -> tt()
r34: a__isPalListKind(i()) -> tt()
r35: a__isPalListKind(nil()) -> tt()
r36: a__isPalListKind(o()) -> tt()
r37: a__isPalListKind(u()) -> tt()
r38: a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2))
r39: a__isQid(a()) -> tt()
r40: a__isQid(e()) -> tt()
r41: a__isQid(i()) -> tt()
r42: a__isQid(o()) -> tt()
r43: a__isQid(u()) -> tt()
r44: mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
r45: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
r46: mark(U12(X)) -> a__U12(mark(X))
r47: mark(isNeList(X)) -> a__isNeList(X)
r48: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
r49: mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
r50: mark(isList(X)) -> a__isList(X)
r51: mark(U23(X)) -> a__U23(mark(X))
r52: mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
r53: mark(U32(X)) -> a__U32(mark(X))
r54: mark(isQid(X)) -> a__isQid(X)
r55: mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
r56: mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
r57: mark(U43(X)) -> a__U43(mark(X))
r58: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
r59: mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
r60: mark(U53(X)) -> a__U53(mark(X))
r61: mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
r62: mark(U62(X)) -> a__U62(mark(X))
r63: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
r64: mark(U72(X)) -> a__U72(mark(X))
r65: mark(isNePal(X)) -> a__isNePal(X)
r66: mark(and(X1,X2)) -> a__and(mark(X1),X2)
r67: mark(isPalListKind(X)) -> a__isPalListKind(X)
r68: mark(isPal(X)) -> a__isPal(X)
r69: mark(nil()) -> nil()
r70: mark(tt()) -> tt()
r71: mark(a()) -> a()
r72: mark(e()) -> e()
r73: mark(i()) -> i()
r74: mark(o()) -> o()
r75: mark(u()) -> u()
r76: a____(X1,X2) -> __(X1,X2)
r77: a__U11(X1,X2) -> U11(X1,X2)
r78: a__U12(X) -> U12(X)
r79: a__isNeList(X) -> isNeList(X)
r80: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
r81: a__U22(X1,X2) -> U22(X1,X2)
r82: a__isList(X) -> isList(X)
r83: a__U23(X) -> U23(X)
r84: a__U31(X1,X2) -> U31(X1,X2)
r85: a__U32(X) -> U32(X)
r86: a__isQid(X) -> isQid(X)
r87: a__U41(X1,X2,X3) -> U41(X1,X2,X3)
r88: a__U42(X1,X2) -> U42(X1,X2)
r89: a__U43(X) -> U43(X)
r90: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
r91: a__U52(X1,X2) -> U52(X1,X2)
r92: a__U53(X) -> U53(X)
r93: a__U61(X1,X2) -> U61(X1,X2)
r94: a__U62(X) -> U62(X)
r95: a__U71(X1,X2) -> U71(X1,X2)
r96: a__U72(X) -> U72(X)
r97: a__isNePal(X) -> isNePal(X)
r98: a__and(X1,X2) -> and(X1,X2)
r99: a__isPalListKind(X) -> isPalListKind(X)
r100: a__isPal(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

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      a____#_A(x1,x2) = ((1,0),(1,0)) x1 + x2 + (0,21)
      ___A(x1,x2) = x1 + x2 + (17,0)
      mark_A(x1) = ((1,0),(1,1)) x1
      a_____A(x1,x2) = x1 + x2 + (17,0)
      nil_A() = (1,0)
      mark#_A(x1) = x1 + (0,20)
      isPal_A(x1) = x1 + (14,1)
      a__isPal#_A(x1) = x1 + (13,19)
      a__isPalListKind#_A(x1) = (0,20)
      a__and#_A(x1,x2) = x2 + (0,20)
      a__isPalListKind_A(x1) = ((0,0),(1,0)) x1
      isPalListKind_A(x1) = ((0,0),(1,0)) x1
      tt_A() = (0,0)
      and_A(x1,x2) = x1 + x2 + (0,17)
      isNePal_A(x1) = x1 + (8,1)
      a__isNePal#_A(x1) = ((1,0),(1,0)) x1 + (7,19)
      a__isQid_A(x1) = ((1,0),(1,0)) x1 + (2,1)
      a__and_A(x1,x2) = x1 + ((1,0),(1,1)) x2 + (0,17)
      U72_A(x1) = x1 + (4,0)
      U71_A(x1,x2) = x1 + x2 + (13,1)
      a__U71#_A(x1,x2) = x1 + x2 + (13,18)
      U62_A(x1) = x1 + (4,1)
      U61_A(x1,x2) = x1 + x2 + (7,0)
      U53_A(x1) = x1 + (1,1)
      U52_A(x1,x2) = x1 + x2 + (15,0)
      a__U52#_A(x1,x2) = x2 + (4,17)
      a__isList#_A(x1) = ((1,0),(1,0)) x1 + (3,1)
      a__U21#_A(x1,x2,x3) = x2 + x3 + (19,19)
      a__U11#_A(x1,x2) = x2 + (2,0)
      a__isNeList#_A(x1) = x1 + (1,19)
      a__U51#_A(x1,x2,x3) = x2 + x3 + (4,18)
      a__U41#_A(x1,x2,x3) = x1 + x2 + x3 + (4,0)
      a__U42#_A(x1,x2) = x2 + (2,21)
      a__isList_A(x1) = ((1,0),(1,0)) x1 + (12,1)
      a__isNeList_A(x1) = ((1,0),(1,0)) x1 + (9,3)
      a__U22#_A(x1,x2) = x1 + x2 + (4,1)
      U51_A(x1,x2,x3) = x1 + x2 + x3 + (25,1)
      U43_A(x1) = x1 + (1,0)
      U42_A(x1,x2) = x1 + x2 + (11,0)
      U41_A(x1,x2,x3) = x1 + x2 + x3 + (24,21)
      U32_A(x1) = x1 + (5,0)
      U31_A(x1,x2) = x1 + x2 + (8,1)
      U23_A(x1) = x1 + (2,0)
      isList_A(x1) = x1 + (12,0)
      U22_A(x1,x2) = x1 + x2 + (15,0)
      U21_A(x1,x2,x3) = x1 + x2 + x3 + (28,0)
      isNeList_A(x1) = x1 + (9,1)
      U12_A(x1) = x1 + (1,0)
      U11_A(x1,x2) = x1 + x2 + (11,1)
      a__U11_A(x1,x2) = x1 + ((1,0),(1,0)) x2 + (11,2)
      a__U12_A(x1) = x1 + (1,0)
      a__U21_A(x1,x2,x3) = x1 + x2 + x3 + (28,0)
      a__U22_A(x1,x2) = x1 + ((1,0),(1,0)) x2 + (15,0)
      a__U23_A(x1) = x1 + (2,1)
      a__U31_A(x1,x2) = x1 + x2 + (8,4)
      a__U32_A(x1) = x1 + (5,5)
      a__U41_A(x1,x2,x3) = x1 + x2 + ((1,0),(1,0)) x3 + (24,21)
      a__U42_A(x1,x2) = x1 + x2 + (11,3)
      a__U43_A(x1) = x1 + (1,0)
      a__U51_A(x1,x2,x3) = x1 + x2 + x3 + (25,2)
      a__U52_A(x1,x2) = x1 + x2 + (15,1)
      a__U53_A(x1) = x1 + (1,1)
      a__U61_A(x1,x2) = x1 + ((1,0),(1,0)) x2 + (7,3)
      a__U62_A(x1) = x1 + (4,4)
      a__U71_A(x1,x2) = x1 + ((1,0),(1,0)) x2 + (13,3)
      a__U72_A(x1) = x1 + (4,3)
      a__isNePal_A(x1) = x1 + (8,2)
      a__isPal_A(x1) = x1 + (14,2)
      a_A() = (1,0)
      e_A() = (1,0)
      i_A() = (0,1)
      o_A() = (1,0)
      u_A() = (1,0)
      isQid_A(x1) = x1 + (2,0)

The next rules are strictly ordered:

  p1, p2, p3, p4, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25, p26, p27, p28, p29, p30, p31, p32, p33, p34, p35, p36, p37, p38, p39, p40, p41, p42, p43, p44, p45, p46, p47, p48, p49, p50, p51, p52, p53, p54, p55, p56, p57, p58, p59, p60, p61, p62, p63, p64, p65, p66, p67, p68, p69, p70, p71

We remove them from the problem.

-- SCC decomposition.

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

p1: a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1)
p2: a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p3: a__and#(tt(),X) -> mark#(X)
p4: mark#(isPalListKind(X)) -> a__isPalListKind#(X)
p5: mark#(and(X1,X2)) -> mark#(X1)
p6: mark#(and(X1,X2)) -> a__and#(mark(X1),X2)

and R consists of:

r1: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
r2: a____(X,nil()) -> mark(X)
r3: a____(nil(),X) -> mark(X)
r4: a__U11(tt(),V) -> a__U12(a__isNeList(V))
r5: a__U12(tt()) -> tt()
r6: a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2)
r7: a__U22(tt(),V2) -> a__U23(a__isList(V2))
r8: a__U23(tt()) -> tt()
r9: a__U31(tt(),V) -> a__U32(a__isQid(V))
r10: a__U32(tt()) -> tt()
r11: a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2)
r12: a__U42(tt(),V2) -> a__U43(a__isNeList(V2))
r13: a__U43(tt()) -> tt()
r14: a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2)
r15: a__U52(tt(),V2) -> a__U53(a__isList(V2))
r16: a__U53(tt()) -> tt()
r17: a__U61(tt(),V) -> a__U62(a__isQid(V))
r18: a__U62(tt()) -> tt()
r19: a__U71(tt(),V) -> a__U72(a__isNePal(V))
r20: a__U72(tt()) -> tt()
r21: a__and(tt(),X) -> mark(X)
r22: a__isList(V) -> a__U11(a__isPalListKind(V),V)
r23: a__isList(nil()) -> tt()
r24: a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r25: a__isNeList(V) -> a__U31(a__isPalListKind(V),V)
r26: a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r27: a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r28: a__isNePal(V) -> a__U61(a__isPalListKind(V),V)
r29: a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
r30: a__isPal(V) -> a__U71(a__isPalListKind(V),V)
r31: a__isPal(nil()) -> tt()
r32: a__isPalListKind(a()) -> tt()
r33: a__isPalListKind(e()) -> tt()
r34: a__isPalListKind(i()) -> tt()
r35: a__isPalListKind(nil()) -> tt()
r36: a__isPalListKind(o()) -> tt()
r37: a__isPalListKind(u()) -> tt()
r38: a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2))
r39: a__isQid(a()) -> tt()
r40: a__isQid(e()) -> tt()
r41: a__isQid(i()) -> tt()
r42: a__isQid(o()) -> tt()
r43: a__isQid(u()) -> tt()
r44: mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
r45: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
r46: mark(U12(X)) -> a__U12(mark(X))
r47: mark(isNeList(X)) -> a__isNeList(X)
r48: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
r49: mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
r50: mark(isList(X)) -> a__isList(X)
r51: mark(U23(X)) -> a__U23(mark(X))
r52: mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
r53: mark(U32(X)) -> a__U32(mark(X))
r54: mark(isQid(X)) -> a__isQid(X)
r55: mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
r56: mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
r57: mark(U43(X)) -> a__U43(mark(X))
r58: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
r59: mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
r60: mark(U53(X)) -> a__U53(mark(X))
r61: mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
r62: mark(U62(X)) -> a__U62(mark(X))
r63: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
r64: mark(U72(X)) -> a__U72(mark(X))
r65: mark(isNePal(X)) -> a__isNePal(X)
r66: mark(and(X1,X2)) -> a__and(mark(X1),X2)
r67: mark(isPalListKind(X)) -> a__isPalListKind(X)
r68: mark(isPal(X)) -> a__isPal(X)
r69: mark(nil()) -> nil()
r70: mark(tt()) -> tt()
r71: mark(a()) -> a()
r72: mark(e()) -> e()
r73: mark(i()) -> i()
r74: mark(o()) -> o()
r75: mark(u()) -> u()
r76: a____(X1,X2) -> __(X1,X2)
r77: a__U11(X1,X2) -> U11(X1,X2)
r78: a__U12(X) -> U12(X)
r79: a__isNeList(X) -> isNeList(X)
r80: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
r81: a__U22(X1,X2) -> U22(X1,X2)
r82: a__isList(X) -> isList(X)
r83: a__U23(X) -> U23(X)
r84: a__U31(X1,X2) -> U31(X1,X2)
r85: a__U32(X) -> U32(X)
r86: a__isQid(X) -> isQid(X)
r87: a__U41(X1,X2,X3) -> U41(X1,X2,X3)
r88: a__U42(X1,X2) -> U42(X1,X2)
r89: a__U43(X) -> U43(X)
r90: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
r91: a__U52(X1,X2) -> U52(X1,X2)
r92: a__U53(X) -> U53(X)
r93: a__U61(X1,X2) -> U61(X1,X2)
r94: a__U62(X) -> U62(X)
r95: a__U71(X1,X2) -> U71(X1,X2)
r96: a__U72(X) -> U72(X)
r97: a__isNePal(X) -> isNePal(X)
r98: a__and(X1,X2) -> and(X1,X2)
r99: a__isPalListKind(X) -> isPalListKind(X)
r100: a__isPal(X) -> isPal(X)

The estimated dependency graph contains the following SCCs:

  {p1, p2, p3, p4, p5, p6}


-- Reduction pair.

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

p1: a__isPalListKind#(__(V1,V2)) -> a__isPalListKind#(V1)
p2: a__isPalListKind#(__(V1,V2)) -> a__and#(a__isPalListKind(V1),isPalListKind(V2))
p3: a__and#(tt(),X) -> mark#(X)
p4: mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
p5: mark#(and(X1,X2)) -> mark#(X1)
p6: mark#(isPalListKind(X)) -> a__isPalListKind#(X)

and R consists of:

r1: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
r2: a____(X,nil()) -> mark(X)
r3: a____(nil(),X) -> mark(X)
r4: a__U11(tt(),V) -> a__U12(a__isNeList(V))
r5: a__U12(tt()) -> tt()
r6: a__U21(tt(),V1,V2) -> a__U22(a__isList(V1),V2)
r7: a__U22(tt(),V2) -> a__U23(a__isList(V2))
r8: a__U23(tt()) -> tt()
r9: a__U31(tt(),V) -> a__U32(a__isQid(V))
r10: a__U32(tt()) -> tt()
r11: a__U41(tt(),V1,V2) -> a__U42(a__isList(V1),V2)
r12: a__U42(tt(),V2) -> a__U43(a__isNeList(V2))
r13: a__U43(tt()) -> tt()
r14: a__U51(tt(),V1,V2) -> a__U52(a__isNeList(V1),V2)
r15: a__U52(tt(),V2) -> a__U53(a__isList(V2))
r16: a__U53(tt()) -> tt()
r17: a__U61(tt(),V) -> a__U62(a__isQid(V))
r18: a__U62(tt()) -> tt()
r19: a__U71(tt(),V) -> a__U72(a__isNePal(V))
r20: a__U72(tt()) -> tt()
r21: a__and(tt(),X) -> mark(X)
r22: a__isList(V) -> a__U11(a__isPalListKind(V),V)
r23: a__isList(nil()) -> tt()
r24: a__isList(__(V1,V2)) -> a__U21(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r25: a__isNeList(V) -> a__U31(a__isPalListKind(V),V)
r26: a__isNeList(__(V1,V2)) -> a__U41(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r27: a__isNeList(__(V1,V2)) -> a__U51(a__and(a__isPalListKind(V1),isPalListKind(V2)),V1,V2)
r28: a__isNePal(V) -> a__U61(a__isPalListKind(V),V)
r29: a__isNePal(__(I,__(P,I))) -> a__and(a__and(a__isQid(I),isPalListKind(I)),and(isPal(P),isPalListKind(P)))
r30: a__isPal(V) -> a__U71(a__isPalListKind(V),V)
r31: a__isPal(nil()) -> tt()
r32: a__isPalListKind(a()) -> tt()
r33: a__isPalListKind(e()) -> tt()
r34: a__isPalListKind(i()) -> tt()
r35: a__isPalListKind(nil()) -> tt()
r36: a__isPalListKind(o()) -> tt()
r37: a__isPalListKind(u()) -> tt()
r38: a__isPalListKind(__(V1,V2)) -> a__and(a__isPalListKind(V1),isPalListKind(V2))
r39: a__isQid(a()) -> tt()
r40: a__isQid(e()) -> tt()
r41: a__isQid(i()) -> tt()
r42: a__isQid(o()) -> tt()
r43: a__isQid(u()) -> tt()
r44: mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
r45: mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
r46: mark(U12(X)) -> a__U12(mark(X))
r47: mark(isNeList(X)) -> a__isNeList(X)
r48: mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3)
r49: mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
r50: mark(isList(X)) -> a__isList(X)
r51: mark(U23(X)) -> a__U23(mark(X))
r52: mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
r53: mark(U32(X)) -> a__U32(mark(X))
r54: mark(isQid(X)) -> a__isQid(X)
r55: mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
r56: mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
r57: mark(U43(X)) -> a__U43(mark(X))
r58: mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
r59: mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
r60: mark(U53(X)) -> a__U53(mark(X))
r61: mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
r62: mark(U62(X)) -> a__U62(mark(X))
r63: mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
r64: mark(U72(X)) -> a__U72(mark(X))
r65: mark(isNePal(X)) -> a__isNePal(X)
r66: mark(and(X1,X2)) -> a__and(mark(X1),X2)
r67: mark(isPalListKind(X)) -> a__isPalListKind(X)
r68: mark(isPal(X)) -> a__isPal(X)
r69: mark(nil()) -> nil()
r70: mark(tt()) -> tt()
r71: mark(a()) -> a()
r72: mark(e()) -> e()
r73: mark(i()) -> i()
r74: mark(o()) -> o()
r75: mark(u()) -> u()
r76: a____(X1,X2) -> __(X1,X2)
r77: a__U11(X1,X2) -> U11(X1,X2)
r78: a__U12(X) -> U12(X)
r79: a__isNeList(X) -> isNeList(X)
r80: a__U21(X1,X2,X3) -> U21(X1,X2,X3)
r81: a__U22(X1,X2) -> U22(X1,X2)
r82: a__isList(X) -> isList(X)
r83: a__U23(X) -> U23(X)
r84: a__U31(X1,X2) -> U31(X1,X2)
r85: a__U32(X) -> U32(X)
r86: a__isQid(X) -> isQid(X)
r87: a__U41(X1,X2,X3) -> U41(X1,X2,X3)
r88: a__U42(X1,X2) -> U42(X1,X2)
r89: a__U43(X) -> U43(X)
r90: a__U51(X1,X2,X3) -> U51(X1,X2,X3)
r91: a__U52(X1,X2) -> U52(X1,X2)
r92: a__U53(X) -> U53(X)
r93: a__U61(X1,X2) -> U61(X1,X2)
r94: a__U62(X) -> U62(X)
r95: a__U71(X1,X2) -> U71(X1,X2)
r96: a__U72(X) -> U72(X)
r97: a__isNePal(X) -> isNePal(X)
r98: a__and(X1,X2) -> and(X1,X2)
r99: a__isPalListKind(X) -> isPalListKind(X)
r100: a__isPal(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

Take the reduction pair:

  matrix interpretations:
  
    carrier: N^2
    order: lexicographic order
    interpretations:
      a__isPalListKind#_A(x1) = ((1,0),(1,1)) x1 + (2,3)
      ___A(x1,x2) = ((1,0),(1,1)) x1 + x2 + (5,4)
      a__and#_A(x1,x2) = ((1,0),(1,1)) x2 + (1,4)
      a__isPalListKind_A(x1) = ((1,0),(1,1)) x1 + (3,2)
      isPalListKind_A(x1) = ((1,0),(1,1)) x1 + (3,1)
      tt_A() = (2,12)
      mark#_A(x1) = ((1,0),(1,1)) x1
      and_A(x1,x2) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + (2,1)
      mark_A(x1) = ((1,0),(1,1)) x1
      a_____A(x1,x2) = ((1,0),(1,1)) x1 + x2 + (5,9)
      nil_A() = (0,0)
      a__U11_A(x1,x2) = x1 + (2,2)
      a__U12_A(x1) = (2,12)
      a__isNeList_A(x1) = (6,10)
      a__U21_A(x1,x2,x3) = x3 + (5,2)
      a__U22_A(x1,x2) = ((0,0),(1,0)) x1 + ((1,0),(1,1)) x2 + (4,7)
      a__isList_A(x1) = ((1,0),(1,0)) x1 + (6,2)
      a__U23_A(x1) = ((0,0),(1,0)) x1 + (3,2)
      a__U31_A(x1,x2) = ((0,0),(1,0)) x1 + (4,8)
      a__U32_A(x1) = (3,11)
      a__isQid_A(x1) = ((1,0),(1,1)) x1 + (0,7)
      a__U41_A(x1,x2,x3) = ((0,0),(1,0)) x1 + (4,1)
      a__U42_A(x1,x2) = (3,4)
      a__U43_A(x1) = (2,13)
      a__U51_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + ((0,0),(1,0)) x3 + (5,3)
      a__U52_A(x1,x2) = ((0,0),(1,0)) x2 + (4,6)
      a__U53_A(x1) = (3,7)
      a__U61_A(x1,x2) = ((1,0),(1,1)) x1 + (2,12)
      a__U62_A(x1) = (3,11)
      a__U71_A(x1,x2) = ((0,0),(1,0)) x2 + (4,3)
      a__U72_A(x1) = (3,4)
      a__isNePal_A(x1) = ((1,0),(1,1)) x1 + (8,16)
      a__and_A(x1,x2) = ((1,0),(1,1)) x1 + ((1,0),(1,0)) x2 + (2,2)
      isPal_A(x1) = (5,1)
      a__isPal_A(x1) = (5,2)
      a_A() = (3,3)
      e_A() = (5,1)
      i_A() = (3,3)
      o_A() = (3,1)
      u_A() = (2,4)
      U11_A(x1,x2) = x1 + (2,1)
      U12_A(x1) = (2,11)
      isNeList_A(x1) = (6,10)
      U21_A(x1,x2,x3) = x3 + (5,1)
      U22_A(x1,x2) = ((0,0),(1,0)) x1 + x2 + (4,3)
      isList_A(x1) = ((1,0),(1,0)) x1 + (6,1)
      U23_A(x1) = ((0,0),(1,0)) x1 + (3,1)
      U31_A(x1,x2) = ((0,0),(1,0)) x1 + (4,8)
      U32_A(x1) = (3,9)
      isQid_A(x1) = x1 + (0,7)
      U41_A(x1,x2,x3) = ((0,0),(1,0)) x1 + (4,1)
      U42_A(x1,x2) = (3,3)
      U43_A(x1) = (2,12)
      U51_A(x1,x2,x3) = ((0,0),(1,0)) x1 + ((0,0),(1,0)) x2 + ((0,0),(1,0)) x3 + (5,2)
      U52_A(x1,x2) = ((0,0),(1,0)) x2 + (4,5)
      U53_A(x1) = (3,6)
      U61_A(x1,x2) = ((1,0),(1,1)) x1 + (2,12)
      U62_A(x1) = (3,9)
      U71_A(x1,x2) = ((0,0),(1,0)) x2 + (4,2)
      U72_A(x1) = (3,3)
      isNePal_A(x1) = x1 + (8,9)

The next rules are strictly ordered:

  p1, p2, p3, p4, p5, p6

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