Termination w.r.t. Q proof of /tmp/tmp7D2to7/PALINDROME_complete_noand

Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.

Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:

MARK(U62(X1, X2)) → A__U62(mark(X1), X2)
MARK(U42(X1, X2, X3)) → A__U42(mark(X1), X2, X3)
MARK(U26(X)) → MARK(X)
MARK(U11(X1, X2)) → MARK(X1)
A__ISNEPAL(__(I, __(P, I))) → A__ISQID(I)
MARK(U51(X1, X2, X3)) → A__U51(mark(X1), X2, X3)
MARK(U81(X1, X2)) → MARK(X1)
A__U45(tt, V2) → A__ISNELIST(V2)
A__ISNELIST(V) → A__U31(a__isPalListKind(V), V)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__U61(tt, V) → A__ISPALLISTKIND(V)
MARK(U41(X1, X2, X3)) → A__U41(mark(X1), X2, X3)
MARK(U74(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(X)
MARK(U23(X1, X2, X3)) → A__U23(mark(X1), X2, X3)
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
A__U73(tt, P) → A__U74(a__isPalListKind(P))
MARK(U81(X1, X2)) → A__U81(mark(X1), X2)
MARK(U63(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
A__U61(tt, V) → A__U62(a__isPalListKind(V), V)
MARK(isNeList(X)) → A__ISNELIST(X)
MARK(U13(X)) → A__U13(mark(X))
MARK(U42(X1, X2, X3)) → MARK(X1)
A__U72(tt, P) → A__U73(a__isPal(P), P)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U53(X1, X2, X3)) → A__U53(mark(X1), X2, X3)
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
A____(__(X, Y), Z) → MARK(Y)
MARK(U73(X1, X2)) → A__U73(mark(X1), X2)
A__U25(tt, V2) → A__U26(a__isList(V2))
A__U32(tt, V) → A__U33(a__isQid(V))
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
MARK(U44(X1, X2, X3)) → A__U44(mark(X1), X2, X3)
MARK(isList(X)) → A__ISLIST(X)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → A__U43(mark(X1), X2, X3)
MARK(U12(X1, X2)) → A__U12(mark(X1), X2)
MARK(U13(X)) → MARK(X)
A__U45(tt, V2) → A__U46(a__isNeList(V2))
A__U24(tt, V1, V2) → A__ISLIST(V1)
MARK(U45(X1, X2)) → A__U45(mark(X1), X2)
MARK(U55(X1, X2)) → A__U55(mark(X1), X2)
A__U41(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U23(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U53(tt, V1, V2) → A__ISPALLISTKIND(V2)
MARK(U62(X1, X2)) → MARK(X1)
A__ISNEPAL(V) → A__ISPALLISTKIND(V)
MARK(isPal(X)) → A__ISPAL(X)
MARK(U46(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(isQid(X)) → A__ISQID(X)
MARK(U73(X1, X2)) → MARK(X1)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
MARK(U82(X1, X2)) → A__U82(mark(X1), X2)
MARK(U33(X)) → MARK(X)
MARK(U31(X1, X2)) → A__U31(mark(X1), X2)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__U21(tt, V1, V2) → A__ISPALLISTKIND(V1)
MARK(__(X1, X2)) → MARK(X2)
A__U11(tt, V) → A__ISPALLISTKIND(V)
A__U44(tt, V1, V2) → A__ISLIST(V1)
MARK(U45(X1, X2)) → MARK(X1)
A__U43(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U72(tt, P) → A__ISPAL(P)
MARK(U24(X1, X2, X3)) → MARK(X1)
A__ISNELIST(V) → A__ISPALLISTKIND(V)
A__U71(tt, I, P) → A__ISPALLISTKIND(I)
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)
A__ISLIST(V) → A__ISPALLISTKIND(V)
A__U51(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U52(tt, V1, V2) → A__ISPALLISTKIND(V2)
MARK(U11(X1, X2)) → A__U11(mark(X1), X2)
A__U82(tt, V) → A__U83(a__isNePal(V))
A__ISNELIST(__(V1, V2)) → A__ISPALLISTKIND(V1)
MARK(U74(X)) → A__U74(mark(X))
MARK(U52(X1, X2, X3)) → A__U52(mark(X1), X2, X3)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__U55(tt, V2) → A__ISLIST(V2)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → A__U22(mark(X1), X2, X3)
MARK(U41(X1, X2, X3)) → MARK(X1)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
A__U82(tt, V) → A__ISNEPAL(V)
MARK(U91(X1, X2)) → MARK(X1)
A__U91(tt, V2) → A__ISPALLISTKIND(V2)
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → A__U92(mark(X))
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
A__U22(tt, V1, V2) → A__ISPALLISTKIND(V2)
MARK(U21(X1, X2, X3)) → MARK(X1)
A____(nil, X) → MARK(X)
A____(X, nil) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
A__U81(tt, V) → A__ISPALLISTKIND(V)
MARK(U83(X)) → A__U83(mark(X))
MARK(U26(X)) → A__U26(mark(X))
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
MARK(U72(X1, X2)) → A__U72(mark(X1), X2)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U56(X)) → A__U56(mark(X))
A__U42(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
A__U12(tt, V) → A__ISNELIST(V)
A____(__(X, Y), Z) → MARK(Z)
A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)
A__U32(tt, V) → A__ISQID(V)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U33(X)) → A__U33(mark(X))
A__U25(tt, V2) → A__ISLIST(V2)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U63(X)) → A__U63(mark(X))
MARK(__(X1, X2)) → MARK(X1)
A__U91(tt, V2) → A__U92(a__isPalListKind(V2))
A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
MARK(U32(X1, X2)) → A__U32(mark(X1), X2)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U46(X)) → A__U46(mark(X))
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U61(X1, X2)) → A__U61(mark(X1), X2)
MARK(U32(X1, X2)) → MARK(X1)
A__U12(tt, V) → A__U13(a__isNeList(V))
A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
MARK(U25(X1, X2)) → A__U25(mark(X1), X2)
A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)
A__ISPAL(V) → A__ISPALLISTKIND(V)
MARK(U91(X1, X2)) → A__U91(mark(X1), X2)
MARK(U25(X1, X2)) → MARK(X1)
MARK(isNePal(X)) → A__ISNEPAL(X)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → A__U54(mark(X1), X2, X3)
A__ISNEPAL(V) → A__U61(a__isPalListKind(V), V)
MARK(U83(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A__U31(tt, V) → A__U32(a__isPalListKind(V), V)
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
MARK(U21(X1, X2, X3)) → A__U21(mark(X1), X2, X3)
A__U31(tt, V) → A__ISPALLISTKIND(V)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U71(X1, X2, X3)) → A__U71(mark(X1), X2, X3)
A__U62(tt, V) → A__U63(a__isQid(V))
MARK(U24(X1, X2, X3)) → A__U24(mark(X1), X2, X3)
A__U62(tt, V) → A__ISQID(V)
A__ISLIST(__(V1, V2)) → A__ISPALLISTKIND(V1)
MARK(isPalListKind(X)) → A__ISPALLISTKIND(X)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U73(tt, P) → A__ISPALLISTKIND(P)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__U55(tt, V2) → A__U56(a__isList(V2))

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

MARK(U62(X1, X2)) → A__U62(mark(X1), X2)
MARK(U42(X1, X2, X3)) → A__U42(mark(X1), X2, X3)
MARK(U26(X)) → MARK(X)
MARK(U11(X1, X2)) → MARK(X1)
A__ISNEPAL(__(I, __(P, I))) → A__ISQID(I)
MARK(U51(X1, X2, X3)) → A__U51(mark(X1), X2, X3)
MARK(U81(X1, X2)) → MARK(X1)
A__U45(tt, V2) → A__ISNELIST(V2)
A__ISNELIST(V) → A__U31(a__isPalListKind(V), V)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__U61(tt, V) → A__ISPALLISTKIND(V)
MARK(U41(X1, X2, X3)) → A__U41(mark(X1), X2, X3)
MARK(U74(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(X)
MARK(U23(X1, X2, X3)) → A__U23(mark(X1), X2, X3)
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
A__U73(tt, P) → A__U74(a__isPalListKind(P))
MARK(U81(X1, X2)) → A__U81(mark(X1), X2)
MARK(U63(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
A__U61(tt, V) → A__U62(a__isPalListKind(V), V)
MARK(isNeList(X)) → A__ISNELIST(X)
MARK(U13(X)) → A__U13(mark(X))
MARK(U42(X1, X2, X3)) → MARK(X1)
A__U72(tt, P) → A__U73(a__isPal(P), P)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U53(X1, X2, X3)) → A__U53(mark(X1), X2, X3)
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
A____(__(X, Y), Z) → MARK(Y)
MARK(U73(X1, X2)) → A__U73(mark(X1), X2)
A__U25(tt, V2) → A__U26(a__isList(V2))
A__U32(tt, V) → A__U33(a__isQid(V))
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
MARK(U44(X1, X2, X3)) → A__U44(mark(X1), X2, X3)
MARK(isList(X)) → A__ISLIST(X)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → A__U43(mark(X1), X2, X3)
MARK(U12(X1, X2)) → A__U12(mark(X1), X2)
MARK(U13(X)) → MARK(X)
A__U45(tt, V2) → A__U46(a__isNeList(V2))
A__U24(tt, V1, V2) → A__ISLIST(V1)
MARK(U45(X1, X2)) → A__U45(mark(X1), X2)
MARK(U55(X1, X2)) → A__U55(mark(X1), X2)
A__U41(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U23(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U53(tt, V1, V2) → A__ISPALLISTKIND(V2)
MARK(U62(X1, X2)) → MARK(X1)
A__ISNEPAL(V) → A__ISPALLISTKIND(V)
MARK(isPal(X)) → A__ISPAL(X)
MARK(U46(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(isQid(X)) → A__ISQID(X)
MARK(U73(X1, X2)) → MARK(X1)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
MARK(U82(X1, X2)) → A__U82(mark(X1), X2)
MARK(U33(X)) → MARK(X)
MARK(U31(X1, X2)) → A__U31(mark(X1), X2)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__U21(tt, V1, V2) → A__ISPALLISTKIND(V1)
MARK(__(X1, X2)) → MARK(X2)
A__U11(tt, V) → A__ISPALLISTKIND(V)
A__U44(tt, V1, V2) → A__ISLIST(V1)
MARK(U45(X1, X2)) → MARK(X1)
A__U43(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U72(tt, P) → A__ISPAL(P)
MARK(U24(X1, X2, X3)) → MARK(X1)
A__ISNELIST(V) → A__ISPALLISTKIND(V)
A__U71(tt, I, P) → A__ISPALLISTKIND(I)
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)
A__ISLIST(V) → A__ISPALLISTKIND(V)
A__U51(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U52(tt, V1, V2) → A__ISPALLISTKIND(V2)
MARK(U11(X1, X2)) → A__U11(mark(X1), X2)
A__U82(tt, V) → A__U83(a__isNePal(V))
A__ISNELIST(__(V1, V2)) → A__ISPALLISTKIND(V1)
MARK(U74(X)) → A__U74(mark(X))
MARK(U52(X1, X2, X3)) → A__U52(mark(X1), X2, X3)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__U55(tt, V2) → A__ISLIST(V2)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → A__U22(mark(X1), X2, X3)
MARK(U41(X1, X2, X3)) → MARK(X1)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
A__U82(tt, V) → A__ISNEPAL(V)
MARK(U91(X1, X2)) → MARK(X1)
A__U91(tt, V2) → A__ISPALLISTKIND(V2)
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → A__U92(mark(X))
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
A__U22(tt, V1, V2) → A__ISPALLISTKIND(V2)
MARK(U21(X1, X2, X3)) → MARK(X1)
A____(nil, X) → MARK(X)
A____(X, nil) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
A__U81(tt, V) → A__ISPALLISTKIND(V)
MARK(U83(X)) → A__U83(mark(X))
MARK(U26(X)) → A__U26(mark(X))
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
MARK(U72(X1, X2)) → A__U72(mark(X1), X2)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U56(X)) → A__U56(mark(X))
A__U42(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
A__U12(tt, V) → A__ISNELIST(V)
A____(__(X, Y), Z) → MARK(Z)
A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)
A__U32(tt, V) → A__ISQID(V)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U33(X)) → A__U33(mark(X))
A__U25(tt, V2) → A__ISLIST(V2)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U63(X)) → A__U63(mark(X))
MARK(__(X1, X2)) → MARK(X1)
A__U91(tt, V2) → A__U92(a__isPalListKind(V2))
A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
MARK(U32(X1, X2)) → A__U32(mark(X1), X2)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U46(X)) → A__U46(mark(X))
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U61(X1, X2)) → A__U61(mark(X1), X2)
MARK(U32(X1, X2)) → MARK(X1)
A__U12(tt, V) → A__U13(a__isNeList(V))
A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
MARK(U25(X1, X2)) → A__U25(mark(X1), X2)
A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)
A__ISPAL(V) → A__ISPALLISTKIND(V)
MARK(U91(X1, X2)) → A__U91(mark(X1), X2)
MARK(U25(X1, X2)) → MARK(X1)
MARK(isNePal(X)) → A__ISNEPAL(X)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → A__U54(mark(X1), X2, X3)
A__ISNEPAL(V) → A__U61(a__isPalListKind(V), V)
MARK(U83(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A__U31(tt, V) → A__U32(a__isPalListKind(V), V)
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
MARK(U21(X1, X2, X3)) → A__U21(mark(X1), X2, X3)
A__U31(tt, V) → A__ISPALLISTKIND(V)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U71(X1, X2, X3)) → A__U71(mark(X1), X2, X3)
A__U62(tt, V) → A__U63(a__isQid(V))
MARK(U24(X1, X2, X3)) → A__U24(mark(X1), X2, X3)
A__U62(tt, V) → A__ISQID(V)
A__ISLIST(__(V1, V2)) → A__ISPALLISTKIND(V1)
MARK(isPalListKind(X)) → A__ISPALLISTKIND(X)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U73(tt, P) → A__ISPALLISTKIND(P)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__U55(tt, V2) → A__U56(a__isList(V2))

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs with 80 less nodes.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ UsableRulesProof

          ↳ QDP

          ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__U91(tt, V2) → A__ISPALLISTKIND(V2)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We can use the usable rules and reduction pair processor [15] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its argument. Then, we can delete all non-usable rules [17] from R.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

            ↳ UsableRulesProof

              ↳ QDP

                ↳ QDPSizeChangeProof

          ↳ QDP

          ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__U91(tt, V2) → A__ISPALLISTKIND(V2)

The TRS R consists of the following rules:

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__U91(a__isPalListKind(V1), V2)
a__isPalListKind(X) → isPalListKind(X)
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U91(X1, X2) → U91(X1, X2)
a__U92(tt) → tt
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)
The graph contains the following edges 1 > 1
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
The graph contains the following edges 1 > 2
A__U91(tt, V2) → A__ISPALLISTKIND(V2)
The graph contains the following edges 2 >= 1

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

            ↳ QDPSizeChangeProof

          ↳ QDP

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
A__U72(tt, P) → A__ISPAL(P)
A__U82(tt, V) → A__ISNEPAL(V)
A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

From the DPs we obtained the following set of size-change graphs:

A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
The graph contains the following edges 3 >= 2
A__U82(tt, V) → A__ISNEPAL(V)
The graph contains the following edges 2 >= 1
A__U72(tt, P) → A__ISPAL(P)
The graph contains the following edges 2 >= 1
A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
The graph contains the following edges 1 > 2, 1 > 3
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
The graph contains the following edges 1 >= 2
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)
The graph contains the following edges 2 >= 2

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPSizeChangeProof

          ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)
A__U44(tt, V1, V2) → A__ISLIST(V1)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
A__U12(tt, V) → A__ISNELIST(V)
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
A__U45(tt, V2) → A__ISNELIST(V2)
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
A__U25(tt, V2) → A__ISLIST(V2)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__U55(tt, V2) → A__ISLIST(V2)
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
A__U24(tt, V1, V2) → A__ISLIST(V1)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

From the DPs we obtained the following set of size-change graphs:

A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
The graph contains the following edges 2 >= 2
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
The graph contains the following edges 1 > 2, 1 > 3
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
The graph contains the following edges 1 > 2, 1 > 3
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U45(tt, V2) → A__ISNELIST(V2)
The graph contains the following edges 2 >= 1
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
The graph contains the following edges 3 >= 2
A__U44(tt, V1, V2) → A__ISLIST(V1)
The graph contains the following edges 2 >= 1
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U54(tt, V1, V2) → A__ISNELIST(V1)
The graph contains the following edges 2 >= 1
A__U12(tt, V) → A__ISNELIST(V)
The graph contains the following edges 2 >= 1
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
The graph contains the following edges 3 >= 2
A__U55(tt, V2) → A__ISLIST(V2)
The graph contains the following edges 2 >= 1
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
The graph contains the following edges 1 >= 2
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
The graph contains the following edges 1 > 2, 1 > 3
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)
The graph contains the following edges 2 >= 2, 3 >= 3
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
The graph contains the following edges 3 >= 2
A__U24(tt, V1, V2) → A__ISLIST(V1)
The graph contains the following edges 2 >= 1
A__U25(tt, V2) → A__ISLIST(V2)
The graph contains the following edges 2 >= 1

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U91(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
A____(nil, X) → MARK(X)
A____(X, nil) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
A____(nil, X) → MARK(X)
A____(X, nil) → MARK(X)
MARK(U82(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.

MARK(U11(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U91(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

Used ordering: Polynomial interpretation with max and min functions [25]:

POL(A____(x₁, x₂)) = x₁ + x₂
POL(MARK(x₁)) = x₁
POL(U11(x₁, x₂)) = x₁
POL(U12(x₁, x₂)) = x₁
POL(U13(x₁)) = x₁
POL(U21(x₁, x₂, x₃)) = x₁
POL(U22(x₁, x₂, x₃)) = x₁
POL(U23(x₁, x₂, x₃)) = x₁
POL(U24(x₁, x₂, x₃)) = x₁
POL(U25(x₁, x₂)) = x₁
POL(U26(x₁)) = x₁
POL(U31(x₁, x₂)) = x₁
POL(U32(x₁, x₂)) = x₁
POL(U33(x₁)) = x₁
POL(U41(x₁, x₂, x₃)) = x₁
POL(U42(x₁, x₂, x₃)) = x₁
POL(U43(x₁, x₂, x₃)) = x₁
POL(U44(x₁, x₂, x₃)) = x₁
POL(U45(x₁, x₂)) = x₁
POL(U46(x₁)) = x₁
POL(U51(x₁, x₂, x₃)) = x₁
POL(U52(x₁, x₂, x₃)) = x₁
POL(U53(x₁, x₂, x₃)) = x₁
POL(U54(x₁, x₂, x₃)) = x₁
POL(U55(x₁, x₂)) = x₁
POL(U56(x₁)) = x₁
POL(U61(x₁, x₂)) = x₁
POL(U62(x₁, x₂)) = x₁
POL(U63(x₁)) = x₁
POL(U71(x₁, x₂, x₃)) = 1 + x₁
POL(U72(x₁, x₂)) = 1 + x₁
POL(U73(x₁, x₂)) = x₁
POL(U74(x₁)) = x₁
POL(U81(x₁, x₂)) = 1 + x₁
POL(U82(x₁, x₂)) = 1 + x₁
POL(U83(x₁)) = x₁
POL(U91(x₁, x₂)) = x₁
POL(U92(x₁)) = x₁
POL(__(x₁, x₂)) = x₁ + x₂
POL(a) = 0
POL(a__U11(x₁, x₂)) = x₁
POL(a__U12(x₁, x₂)) = x₁
POL(a__U13(x₁)) = x₁
POL(a__U21(x₁, x₂, x₃)) = x₁
POL(a__U22(x₁, x₂, x₃)) = x₁
POL(a__U23(x₁, x₂, x₃)) = x₁
POL(a__U24(x₁, x₂, x₃)) = x₁
POL(a__U25(x₁, x₂)) = x₁
POL(a__U26(x₁)) = x₁
POL(a__U31(x₁, x₂)) = x₁
POL(a__U32(x₁, x₂)) = x₁
POL(a__U33(x₁)) = x₁
POL(a__U41(x₁, x₂, x₃)) = x₁
POL(a__U42(x₁, x₂, x₃)) = x₁
POL(a__U43(x₁, x₂, x₃)) = x₁
POL(a__U44(x₁, x₂, x₃)) = x₁
POL(a__U45(x₁, x₂)) = x₁
POL(a__U46(x₁)) = x₁
POL(a__U51(x₁, x₂, x₃)) = x₁
POL(a__U52(x₁, x₂, x₃)) = x₁
POL(a__U53(x₁, x₂, x₃)) = x₁
POL(a__U54(x₁, x₂, x₃)) = x₁
POL(a__U55(x₁, x₂)) = x₁
POL(a__U56(x₁)) = x₁
POL(a__U61(x₁, x₂)) = x₁
POL(a__U62(x₁, x₂)) = x₁
POL(a__U63(x₁)) = x₁
POL(a__U71(x₁, x₂, x₃)) = 1 + x₁
POL(a__U72(x₁, x₂)) = 1 + x₁
POL(a__U73(x₁, x₂)) = x₁
POL(a__U74(x₁)) = x₁
POL(a__U81(x₁, x₂)) = 1 + x₁
POL(a__U82(x₁, x₂)) = 1 + x₁
POL(a__U83(x₁)) = x₁
POL(a__U91(x₁, x₂)) = x₁
POL(a__U92(x₁)) = x₁
POL(a____(x₁, x₂)) = x₁ + x₂
POL(a__isList(x₁)) = 0
POL(a__isNeList(x₁)) = 0
POL(a__isNePal(x₁)) = 1
POL(a__isPal(x₁)) = 1
POL(a__isPalListKind(x₁)) = 0
POL(a__isQid(x₁)) = 0
POL(e) = 0
POL(i) = 0
POL(isList(x₁)) = 0
POL(isNeList(x₁)) = 0
POL(isNePal(x₁)) = 1
POL(isPal(x₁)) = 1
POL(isPalListKind(x₁)) = 0
POL(isQid(x₁)) = 0
POL(mark(x₁)) = x₁
POL(nil) = 1
POL(o) = 0
POL(tt) = 0
POL(u) = 0

The following usable rules [17] were oriented:

a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U82(X1, X2) → U82(X1, X2)
a__U81(X1, X2) → U81(X1, X2)
a__U74(X) → U74(X)
a__isPal(X) → isPal(X)
a__U73(X1, X2) → U73(X1, X2)
a__U72(X1, X2) → U72(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U92(X) → U92(X)
a__U91(X1, X2) → U91(X1, X2)
a__isNePal(X) → isNePal(X)
a__U83(X) → U83(X)
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
a__U13(X) → U13(X)
a__isPalListKind(X) → isPalListKind(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__isNeList(X) → isNeList(X)
a____(X1, X2) → __(X1, X2)
mark(u) → u
a__U12(X1, X2) → U12(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U26(X) → U26(X)
a__isList(X) → isList(X)
a__U32(X1, X2) → U32(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U26(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U32(tt, V) → a__U33(a__isQid(V))
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
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__isPalListKind(V), V)
a__U13(tt) → tt
a__U12(tt, V) → a__U13(a__isNeList(V))
a__isQid(u) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(a) → tt
a__isQid(e) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isList(nil) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__U92(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U83(tt) → tt
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U74(tt) → tt
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(isQid(X)) → a__isQid(X)
mark(U33(X)) → a__U33(mark(X))
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U26(X)) → a__U26(mark(X))
mark(isList(X)) → a__isList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U13(X)) → a__U13(mark(X))
mark(isPalListKind(X)) → a__isPalListKind(X)

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

MARK(U26(X)) → MARK(X)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U83(X)) → MARK(X)
MARK(U46(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

MARK(U63(X)) → MARK(X)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U61(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.

MARK(U26(X)) → MARK(X)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U83(X)) → MARK(X)
MARK(U46(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

Used ordering: Polynomial interpretation with max and min functions [25]:

POL(A____(x₁, x₂)) = x₁ + x₂
POL(MARK(x₁)) = x₁
POL(U11(x₁, x₂)) = x₁
POL(U12(x₁, x₂)) = x₁
POL(U13(x₁)) = x₁
POL(U21(x₁, x₂, x₃)) = x₁
POL(U22(x₁, x₂, x₃)) = x₁
POL(U23(x₁, x₂, x₃)) = x₁
POL(U24(x₁, x₂, x₃)) = x₁
POL(U25(x₁, x₂)) = x₁
POL(U26(x₁)) = x₁
POL(U31(x₁, x₂)) = x₁
POL(U32(x₁, x₂)) = x₁
POL(U33(x₁)) = x₁
POL(U41(x₁, x₂, x₃)) = x₁
POL(U42(x₁, x₂, x₃)) = x₁
POL(U43(x₁, x₂, x₃)) = x₁
POL(U44(x₁, x₂, x₃)) = x₁
POL(U45(x₁, x₂)) = x₁
POL(U46(x₁)) = x₁
POL(U51(x₁, x₂, x₃)) = x₁
POL(U52(x₁, x₂, x₃)) = x₁
POL(U53(x₁, x₂, x₃)) = x₁
POL(U54(x₁, x₂, x₃)) = x₁
POL(U55(x₁, x₂)) = x₁
POL(U56(x₁)) = x₁
POL(U61(x₁, x₂)) = 1 + x₁ + x₂
POL(U62(x₁, x₂)) = 1 + x₁ + x₂
POL(U63(x₁)) = 1 + x₁
POL(U71(x₁, x₂, x₃)) = 1 + x₁ + x₃
POL(U72(x₁, x₂)) = 1 + x₂
POL(U73(x₁, x₂)) = x₁
POL(U74(x₁)) = x₁
POL(U81(x₁, x₂)) = 1 + x₂
POL(U82(x₁, x₂)) = 1 + x₁ + x₂
POL(U83(x₁)) = x₁
POL(U91(x₁, x₂)) = x₁
POL(U92(x₁)) = x₁
POL(__(x₁, x₂)) = x₁ + x₂
POL(a) = 0
POL(a__U11(x₁, x₂)) = x₁
POL(a__U12(x₁, x₂)) = x₁
POL(a__U13(x₁)) = x₁
POL(a__U21(x₁, x₂, x₃)) = x₁
POL(a__U22(x₁, x₂, x₃)) = x₁
POL(a__U23(x₁, x₂, x₃)) = x₁
POL(a__U24(x₁, x₂, x₃)) = x₁
POL(a__U25(x₁, x₂)) = x₁
POL(a__U26(x₁)) = x₁
POL(a__U31(x₁, x₂)) = x₁
POL(a__U32(x₁, x₂)) = x₁
POL(a__U33(x₁)) = x₁
POL(a__U41(x₁, x₂, x₃)) = x₁
POL(a__U42(x₁, x₂, x₃)) = x₁
POL(a__U43(x₁, x₂, x₃)) = x₁
POL(a__U44(x₁, x₂, x₃)) = x₁
POL(a__U45(x₁, x₂)) = x₁
POL(a__U46(x₁)) = x₁
POL(a__U51(x₁, x₂, x₃)) = x₁
POL(a__U52(x₁, x₂, x₃)) = x₁
POL(a__U53(x₁, x₂, x₃)) = x₁
POL(a__U54(x₁, x₂, x₃)) = x₁
POL(a__U55(x₁, x₂)) = x₁
POL(a__U56(x₁)) = x₁
POL(a__U61(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U62(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U63(x₁)) = 1 + x₁
POL(a__U71(x₁, x₂, x₃)) = 1 + x₁ + x₃
POL(a__U72(x₁, x₂)) = 1 + x₂
POL(a__U73(x₁, x₂)) = x₁
POL(a__U74(x₁)) = x₁
POL(a__U81(x₁, x₂)) = 1 + x₂
POL(a__U82(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U83(x₁)) = x₁
POL(a__U91(x₁, x₂)) = x₁
POL(a__U92(x₁)) = x₁
POL(a____(x₁, x₂)) = x₁ + x₂
POL(a__isList(x₁)) = 0
POL(a__isNeList(x₁)) = 0
POL(a__isNePal(x₁)) = 1 + x₁
POL(a__isPal(x₁)) = 1 + x₁
POL(a__isPalListKind(x₁)) = 0
POL(a__isQid(x₁)) = 0
POL(e) = 1
POL(i) = 0
POL(isList(x₁)) = 0
POL(isNeList(x₁)) = 0
POL(isNePal(x₁)) = 1 + x₁
POL(isPal(x₁)) = 1 + x₁
POL(isPalListKind(x₁)) = 0
POL(isQid(x₁)) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(tt) = 0
POL(u) = 0

The following usable rules [17] were oriented:

a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U82(X1, X2) → U82(X1, X2)
a__U81(X1, X2) → U81(X1, X2)
a__U74(X) → U74(X)
a__isPal(X) → isPal(X)
a__U73(X1, X2) → U73(X1, X2)
a__U72(X1, X2) → U72(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U92(X) → U92(X)
a__U91(X1, X2) → U91(X1, X2)
a__isNePal(X) → isNePal(X)
a__U83(X) → U83(X)
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
a__U13(X) → U13(X)
a__isPalListKind(X) → isPalListKind(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__isNeList(X) → isNeList(X)
a____(X1, X2) → __(X1, X2)
mark(u) → u
a__U12(X1, X2) → U12(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U26(X) → U26(X)
a__isList(X) → isList(X)
a__U32(X1, X2) → U32(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U26(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U32(tt, V) → a__U33(a__isQid(V))
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
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__isPalListKind(V), V)
a__U13(tt) → tt
a__U12(tt, V) → a__U13(a__isNeList(V))
a__isQid(u) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(a) → tt
a__isQid(e) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isList(nil) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__U92(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U83(tt) → tt
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U74(tt) → tt
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(isQid(X)) → a__isQid(X)
mark(U33(X)) → a__U33(mark(X))
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U26(X)) → a__U26(mark(X))
mark(isList(X)) → a__isList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U13(X)) → a__U13(mark(X))
mark(isPalListKind(X)) → a__isPalListKind(X)

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

                  ↳ QDP

                    ↳ QDPOrderProof

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

MARK(U11(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U92(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

MARK(U26(X)) → MARK(X)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

The remaining pairs can at least be oriented weakly.

MARK(U11(X1, X2)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)

Used ordering: Polynomial interpretation [25]:

POL(A____(x₁, x₂)) = x₁ + x₂
POL(MARK(x₁)) = x₁
POL(U11(x₁, x₂)) = x₁ + x₂
POL(U12(x₁, x₂)) = x₁ + x₂
POL(U13(x₁)) = x₁
POL(U21(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U22(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U23(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U24(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U25(x₁, x₂)) = 1 + x₁ + x₂
POL(U26(x₁)) = 1 + x₁
POL(U31(x₁, x₂)) = x₁ + x₂
POL(U32(x₁, x₂)) = x₁ + x₂
POL(U33(x₁)) = x₁
POL(U41(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U42(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U43(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U44(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U45(x₁, x₂)) = 1 + x₁ + x₂
POL(U46(x₁)) = x₁
POL(U51(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U52(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U53(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U54(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U55(x₁, x₂)) = 1 + x₁ + x₂
POL(U56(x₁)) = x₁
POL(U61(x₁, x₂)) = 0
POL(U62(x₁, x₂)) = 0
POL(U63(x₁)) = 0
POL(U71(x₁, x₂, x₃)) = 0
POL(U72(x₁, x₂)) = 0
POL(U73(x₁, x₂)) = x₁
POL(U74(x₁)) = x₁
POL(U81(x₁, x₂)) = x₁
POL(U82(x₁, x₂)) = 0
POL(U83(x₁)) = x₁
POL(U91(x₁, x₂)) = x₁
POL(U92(x₁)) = x₁
POL(__(x₁, x₂)) = 1 + x₁ + x₂
POL(a) = 0
POL(a__U11(x₁, x₂)) = x₁ + x₂
POL(a__U12(x₁, x₂)) = x₁ + x₂
POL(a__U13(x₁)) = x₁
POL(a__U21(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U22(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U23(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U24(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U25(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U26(x₁)) = 1 + x₁
POL(a__U31(x₁, x₂)) = x₁ + x₂
POL(a__U32(x₁, x₂)) = x₁ + x₂
POL(a__U33(x₁)) = x₁
POL(a__U41(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U42(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U43(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U44(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U45(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U46(x₁)) = x₁
POL(a__U51(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U52(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U53(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U54(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U55(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U56(x₁)) = x₁
POL(a__U61(x₁, x₂)) = 0
POL(a__U62(x₁, x₂)) = 0
POL(a__U63(x₁)) = 0
POL(a__U71(x₁, x₂, x₃)) = 0
POL(a__U72(x₁, x₂)) = 0
POL(a__U73(x₁, x₂)) = x₁
POL(a__U74(x₁)) = x₁
POL(a__U81(x₁, x₂)) = x₁
POL(a__U82(x₁, x₂)) = 0
POL(a__U83(x₁)) = x₁
POL(a__U91(x₁, x₂)) = x₁
POL(a__U92(x₁)) = x₁
POL(a____(x₁, x₂)) = 1 + x₁ + x₂
POL(a__isList(x₁)) = x₁
POL(a__isNeList(x₁)) = x₁
POL(a__isNePal(x₁)) = 0
POL(a__isPal(x₁)) = 0
POL(a__isPalListKind(x₁)) = 0
POL(a__isQid(x₁)) = 0
POL(e) = 0
POL(i) = 0
POL(isList(x₁)) = x₁
POL(isNeList(x₁)) = x₁
POL(isNePal(x₁)) = 0
POL(isPal(x₁)) = 0
POL(isPalListKind(x₁)) = 0
POL(isQid(x₁)) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(tt) = 0
POL(u) = 0

The following usable rules [17] were oriented:

a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U82(X1, X2) → U82(X1, X2)
a__U81(X1, X2) → U81(X1, X2)
a__U74(X) → U74(X)
a__isPal(X) → isPal(X)
a__U73(X1, X2) → U73(X1, X2)
a__U72(X1, X2) → U72(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U92(X) → U92(X)
a__U91(X1, X2) → U91(X1, X2)
a__isNePal(X) → isNePal(X)
a__U83(X) → U83(X)
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
a__U13(X) → U13(X)
a__isPalListKind(X) → isPalListKind(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__isNeList(X) → isNeList(X)
a____(X1, X2) → __(X1, X2)
mark(u) → u
a__U12(X1, X2) → U12(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U26(X) → U26(X)
a__isList(X) → isList(X)
a__U32(X1, X2) → U32(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U26(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U32(tt, V) → a__U33(a__isQid(V))
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
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__isPalListKind(V), V)
a__U13(tt) → tt
a__U12(tt, V) → a__U13(a__isNeList(V))
a__isQid(u) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(a) → tt
a__isQid(e) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isList(nil) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__U92(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U83(tt) → tt
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U74(tt) → tt
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(isQid(X)) → a__isQid(X)
mark(U33(X)) → a__U33(mark(X))
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U26(X)) → a__U26(mark(X))
mark(isList(X)) → a__isList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U13(X)) → a__U13(mark(X))
mark(isPalListKind(X)) → a__isPalListKind(X)

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

                  ↳ QDP

                    ↳ QDPOrderProof

                      ↳ QDP

                        ↳ DependencyGraphProof

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

                  ↳ QDP

                    ↳ QDPOrderProof

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ AND

                            ↳ QDP

                              ↳ QDPOrderProof

                            ↳ QDP

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))

The remaining pairs can at least be oriented weakly.
none
Used ordering: Polynomial interpretation with max and min functions [25]:

POL(A____(x₁, x₂)) = x₁
POL(U11(x₁, x₂)) = x₁
POL(U12(x₁, x₂)) = 0
POL(U13(x₁)) = 0
POL(U21(x₁, x₂, x₃)) = x₂ + x₃
POL(U22(x₁, x₂, x₃)) = x₃
POL(U23(x₁, x₂, x₃)) = 0
POL(U24(x₁, x₂, x₃)) = 0
POL(U25(x₁, x₂)) = 0
POL(U26(x₁)) = 0
POL(U31(x₁, x₂)) = 1 + x₂
POL(U32(x₁, x₂)) = x₂
POL(U33(x₁)) = 0
POL(U41(x₁, x₂, x₃)) = x₂
POL(U42(x₁, x₂, x₃)) = 0
POL(U43(x₁, x₂, x₃)) = 0
POL(U44(x₁, x₂, x₃)) = 0
POL(U45(x₁, x₂)) = 0
POL(U46(x₁)) = 0
POL(U51(x₁, x₂, x₃)) = x₂ + x₃
POL(U52(x₁, x₂, x₃)) = x₃
POL(U53(x₁, x₂, x₃)) = 0
POL(U54(x₁, x₂, x₃)) = 0
POL(U55(x₁, x₂)) = 0
POL(U56(x₁)) = 0
POL(U61(x₁, x₂)) = 0
POL(U62(x₁, x₂)) = 0
POL(U63(x₁)) = 0
POL(U71(x₁, x₂, x₃)) = 0
POL(U72(x₁, x₂)) = 0
POL(U73(x₁, x₂)) = 0
POL(U74(x₁)) = 0
POL(U81(x₁, x₂)) = 0
POL(U82(x₁, x₂)) = 0
POL(U83(x₁)) = 0
POL(U91(x₁, x₂)) = 0
POL(U92(x₁)) = x₁
POL(__(x₁, x₂)) = 1 + x₁ + x₂
POL(a) = 0
POL(a__U11(x₁, x₂)) = x₁
POL(a__U12(x₁, x₂)) = 0
POL(a__U13(x₁)) = 0
POL(a__U21(x₁, x₂, x₃)) = x₂ + x₃
POL(a__U22(x₁, x₂, x₃)) = x₃
POL(a__U23(x₁, x₂, x₃)) = 0
POL(a__U24(x₁, x₂, x₃)) = 0
POL(a__U25(x₁, x₂)) = 0
POL(a__U26(x₁)) = 0
POL(a__U31(x₁, x₂)) = 1 + x₂
POL(a__U32(x₁, x₂)) = x₂
POL(a__U33(x₁)) = 0
POL(a__U41(x₁, x₂, x₃)) = x₂
POL(a__U42(x₁, x₂, x₃)) = 0
POL(a__U43(x₁, x₂, x₃)) = 0
POL(a__U44(x₁, x₂, x₃)) = 0
POL(a__U45(x₁, x₂)) = 0
POL(a__U46(x₁)) = 0
POL(a__U51(x₁, x₂, x₃)) = x₂ + x₃
POL(a__U52(x₁, x₂, x₃)) = x₃
POL(a__U53(x₁, x₂, x₃)) = 0
POL(a__U54(x₁, x₂, x₃)) = 0
POL(a__U55(x₁, x₂)) = 0
POL(a__U56(x₁)) = 0
POL(a__U61(x₁, x₂)) = 0
POL(a__U62(x₁, x₂)) = 0
POL(a__U63(x₁)) = 0
POL(a__U71(x₁, x₂, x₃)) = 0
POL(a__U72(x₁, x₂)) = 0
POL(a__U73(x₁, x₂)) = 0
POL(a__U74(x₁)) = 0
POL(a__U81(x₁, x₂)) = 0
POL(a__U82(x₁, x₂)) = 0
POL(a__U83(x₁)) = 0
POL(a__U91(x₁, x₂)) = 0
POL(a__U92(x₁)) = x₁
POL(a____(x₁, x₂)) = 1 + x₁ + x₂
POL(a__isList(x₁)) = x₁
POL(a__isNeList(x₁)) = 1 + x₁
POL(a__isNePal(x₁)) = 0
POL(a__isPal(x₁)) = 1
POL(a__isPalListKind(x₁)) = 0
POL(a__isQid(x₁)) = 0
POL(e) = 0
POL(i) = 0
POL(isList(x₁)) = x₁
POL(isNeList(x₁)) = 1 + x₁
POL(isNePal(x₁)) = 0
POL(isPal(x₁)) = 1
POL(isPalListKind(x₁)) = 0
POL(isQid(x₁)) = 0
POL(mark(x₁)) = x₁
POL(nil) = 1
POL(o) = 0
POL(tt) = 0
POL(u) = 0

The following usable rules [17] were oriented:

a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U82(X1, X2) → U82(X1, X2)
a__U81(X1, X2) → U81(X1, X2)
a__U74(X) → U74(X)
a__isPal(X) → isPal(X)
a__U73(X1, X2) → U73(X1, X2)
a__U72(X1, X2) → U72(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U92(X) → U92(X)
a__U91(X1, X2) → U91(X1, X2)
a__isNePal(X) → isNePal(X)
a__U83(X) → U83(X)
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
a__U13(X) → U13(X)
a__isPalListKind(X) → isPalListKind(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__isNeList(X) → isNeList(X)
a____(X1, X2) → __(X1, X2)
mark(u) → u
a__U12(X1, X2) → U12(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U26(X) → U26(X)
a__isList(X) → isList(X)
a__U32(X1, X2) → U32(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U26(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U32(tt, V) → a__U33(a__isQid(V))
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
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__isPalListKind(V), V)
a__U13(tt) → tt
a__U12(tt, V) → a__U13(a__isNeList(V))
a__isQid(u) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(a) → tt
a__isQid(e) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isList(nil) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__U92(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U83(tt) → tt
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U74(tt) → tt
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(isQid(X)) → a__isQid(X)
mark(U33(X)) → a__U33(mark(X))
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U26(X)) → a__U26(mark(X))
mark(isList(X)) → a__isList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U13(X)) → a__U13(mark(X))
mark(isPalListKind(X)) → a__isPalListKind(X)

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

                  ↳ QDP

                    ↳ QDPOrderProof

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ AND

                            ↳ QDP

                              ↳ QDPOrderProof

                                ↳ QDP

                                  ↳ PisEmptyProof

                            ↳ QDP

            ↳ QDPOrderProof

Q DP problem:
P is empty.
The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The TRS P is empty. Hence, there is no (P,Q,R) chain.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

                  ↳ QDP

                    ↳ QDPOrderProof

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ AND

                            ↳ QDP

                            ↳ QDP

                              ↳ UsableRulesProof

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

              ↳ QDP

                ↳ QDPOrderProof

                  ↳ QDP

                    ↳ QDPOrderProof

                      ↳ QDP

                        ↳ DependencyGraphProof

                          ↳ AND

                            ↳ QDP

                            ↳ QDP

                              ↳ UsableRulesProof

                                ↳ QDP

                                  ↳ QDPSizeChangeProof

            ↳ QDPOrderProof

Q DP problem:
The TRS P consists of the following rules:

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U13(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs:

MARK(U12(X1, X2)) → MARK(X1)
The graph contains the following edges 1 > 1
MARK(U11(X1, X2)) → MARK(X1)
The graph contains the following edges 1 > 1
MARK(U83(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U31(X1, X2)) → MARK(X1)
The graph contains the following edges 1 > 1
MARK(U46(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U91(X1, X2)) → MARK(X1)
The graph contains the following edges 1 > 1
MARK(U56(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U92(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U73(X1, X2)) → MARK(X1)
The graph contains the following edges 1 > 1
MARK(U33(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U74(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U13(X)) → MARK(X)
The graph contains the following edges 1 > 1
MARK(U32(X1, X2)) → MARK(X1)
The graph contains the following edges 1 > 1

We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U45(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Z)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
MARK(U46(X)) → MARK(X)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
A____(nil, X) → MARK(X)
A____(X, nil) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X2)

The remaining pairs can at least be oriented weakly.

MARK(U11(X1, X2)) → MARK(X1)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U32(X1, X2)) → MARK(X1)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)

Used ordering: Polynomial interpretation [25]:

POL(A____(x₁, x₂)) = 1 + x₁ + x₂
POL(MARK(x₁)) = x₁
POL(U11(x₁, x₂)) = x₁ + x₂
POL(U12(x₁, x₂)) = x₁ + x₂
POL(U13(x₁)) = x₁
POL(U21(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U22(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U23(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U24(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U25(x₁, x₂)) = 1 + x₁ + x₂
POL(U26(x₁)) = 1 + x₁
POL(U31(x₁, x₂)) = x₁ + x₂
POL(U32(x₁, x₂)) = x₁ + x₂
POL(U33(x₁)) = 1 + x₁
POL(U41(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U42(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U43(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U44(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U45(x₁, x₂)) = 1 + x₁ + x₂
POL(U46(x₁)) = 1 + x₁
POL(U51(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U52(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U53(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U54(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(U55(x₁, x₂)) = 1 + x₁ + x₂
POL(U56(x₁)) = 1 + x₁
POL(U61(x₁, x₂)) = x₁ + x₂
POL(U62(x₁, x₂)) = x₁ + x₂
POL(U63(x₁)) = 1 + x₁
POL(U71(x₁, x₂, x₃)) = 1 + x₁ + x₃
POL(U72(x₁, x₂)) = 1 + x₁ + x₂
POL(U73(x₁, x₂)) = 1 + x₁
POL(U74(x₁)) = 1 + x₁
POL(U81(x₁, x₂)) = x₁ + x₂
POL(U82(x₁, x₂)) = x₁ + x₂
POL(U83(x₁)) = x₁
POL(U91(x₁, x₂)) = x₁
POL(U92(x₁)) = x₁
POL(__(x₁, x₂)) = 1 + x₁ + x₂
POL(a) = 1
POL(a__U11(x₁, x₂)) = x₁ + x₂
POL(a__U12(x₁, x₂)) = x₁ + x₂
POL(a__U13(x₁)) = x₁
POL(a__U21(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U22(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U23(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U24(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U25(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U26(x₁)) = 1 + x₁
POL(a__U31(x₁, x₂)) = x₁ + x₂
POL(a__U32(x₁, x₂)) = x₁ + x₂
POL(a__U33(x₁)) = 1 + x₁
POL(a__U41(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U42(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U43(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U44(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U45(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U46(x₁)) = 1 + x₁
POL(a__U51(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U52(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U53(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U54(x₁, x₂, x₃)) = 1 + x₁ + x₂ + x₃
POL(a__U55(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U56(x₁)) = 1 + x₁
POL(a__U61(x₁, x₂)) = x₁ + x₂
POL(a__U62(x₁, x₂)) = x₁ + x₂
POL(a__U63(x₁)) = 1 + x₁
POL(a__U71(x₁, x₂, x₃)) = 1 + x₁ + x₃
POL(a__U72(x₁, x₂)) = 1 + x₁ + x₂
POL(a__U73(x₁, x₂)) = 1 + x₁
POL(a__U74(x₁)) = 1 + x₁
POL(a__U81(x₁, x₂)) = x₁ + x₂
POL(a__U82(x₁, x₂)) = x₁ + x₂
POL(a__U83(x₁)) = x₁
POL(a__U91(x₁, x₂)) = x₁
POL(a__U92(x₁)) = x₁
POL(a____(x₁, x₂)) = 1 + x₁ + x₂
POL(a__isList(x₁)) = 1 + x₁
POL(a__isNeList(x₁)) = 1 + x₁
POL(a__isNePal(x₁)) = 1 + x₁
POL(a__isPal(x₁)) = 1 + x₁
POL(a__isPalListKind(x₁)) = 1
POL(a__isQid(x₁)) = x₁
POL(e) = 1
POL(i) = 1
POL(isList(x₁)) = 1 + x₁
POL(isNeList(x₁)) = 1 + x₁
POL(isNePal(x₁)) = 1 + x₁
POL(isPal(x₁)) = 1 + x₁
POL(isPalListKind(x₁)) = 1
POL(isQid(x₁)) = x₁
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 1
POL(tt) = 1
POL(u) = 1

The following usable rules [17] were oriented:

a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U82(X1, X2) → U82(X1, X2)
a__U81(X1, X2) → U81(X1, X2)
a__U74(X) → U74(X)
a__isPal(X) → isPal(X)
a__U73(X1, X2) → U73(X1, X2)
a__U72(X1, X2) → U72(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U92(X) → U92(X)
a__U91(X1, X2) → U91(X1, X2)
a__isNePal(X) → isNePal(X)
a__U83(X) → U83(X)
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
a__U13(X) → U13(X)
a__isPalListKind(X) → isPalListKind(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__isNeList(X) → isNeList(X)
a____(X1, X2) → __(X1, X2)
mark(u) → u
a__U12(X1, X2) → U12(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U26(X) → U26(X)
a__isList(X) → isList(X)
a__U32(X1, X2) → U32(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U26(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U32(tt, V) → a__U33(a__isQid(V))
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
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__isPalListKind(V), V)
a__U13(tt) → tt
a__U12(tt, V) → a__U13(a__isNeList(V))
a__isQid(u) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(a) → tt
a__isQid(e) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isList(nil) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__U92(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U83(tt) → tt
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U74(tt) → tt
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(isQid(X)) → a__isQid(X)
mark(U33(X)) → a__U33(mark(X))
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U26(X)) → a__U26(mark(X))
mark(isList(X)) → a__isList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U13(X)) → a__U13(mark(X))
mark(isPalListKind(X)) → a__isPalListKind(X)

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

        ↳ AND

          ↳ QDP

          ↳ QDP

          ↳ QDP

          ↳ QDP

            ↳ QDPOrderProof

            ↳ QDPOrderProof

              ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U82(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U32(X1, X2)) → MARK(X1)

The TRS R consists of the following rules:

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__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(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__U91(a__isPalListKind(V1), 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(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(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(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.
We have to consider all minimal (P,Q,R)-chains.