Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

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.

(1) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(2) Obligation:

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

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

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.

(3) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs with 80 less nodes.

(4) Complex Obligation (AND)

(5) Obligation:

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

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

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.

(6) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A__U91(x1, x2)  =  x2
tt  =  tt
A__ISPALLISTKIND(x1)  =  x1
__(x1, x2)  =  __(x1, x2)
a__isPalListKind(x1)  =  a__isPalListKind
nil  =  nil
o  =  o
a__U91(x1, x2)  =  a__U91
a__U92(x1)  =  x1
e  =  e
i  =  i
a  =  a
U91(x1, x2)  =  U91(x2)
isPalListKind(x1)  =  isPalListKind(x1)
U92(x1)  =  U92
u  =  u

Lexicographic Path Order [LPO].
Precedence:

a_U91 > [tt, a_{isPalListKind}, nil, o]
u > [tt, a_{isPalListKind}, nil, o]

The following usable rules [FROCOS05] were oriented: none

(7) Obligation:

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

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.

(8) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(9) TRUE

(10) Obligation:

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

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

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

(11) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A__ISNEPAL(x1)  =  x1
__(x1, x2)  =  __(x1, x2)
A__U71(x1, x2, x3)  =  A__U71(x1, x2, x3)
a__isQid(x1)  =  a__isQid(x1)
tt  =  tt
A__U72(x1, x2)  =  A__U72(x1, x2)
a__isPalListKind(x1)  =  a__isPalListKind(x1)
A__ISPAL(x1)  =  A__ISPAL(x1)
A__U81(x1, x2)  =  A__U81(x2)
A__U82(x1, x2)  =  A__U82(x2)
nil  =  nil
o  =  o
e  =  e
i  =  i
a  =  a
isPalListKind(x1)  =  isPalListKind(x1)
a__U92(x1)  =  a__U92
a__U91(x1, x2)  =  a__U91(x1, x2)
isQid(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92
u  =  u

Lexicographic Path Order [LPO].
Precedence:

_₂ > A_U713 > [tt, A_U722, a_{isPalListKind1}, i, isPalListKind₁] > A_ISPAL1 > [A_U811, A_U821]
_₂ > a_isQid1 > [tt, A_U722, a_{isPalListKind1}, i, isPalListKind₁] > A_ISPAL1 > [A_U811, A_U821]
_₂ > [a_U92, a_U912, U91₂] > [tt, A_U722, a_{isPalListKind1}, i, isPalListKind₁] > A_ISPAL1 > [A_U811, A_U821]
_₂ > [a_U92, a_U912, U91₂] > U92
e > [tt, A_U722, a_{isPalListKind1}, i, isPalListKind₁] > A_ISPAL1 > [A_U811, A_U821]

The following usable rules [FROCOS05] were oriented:

a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(a) → tt
a__isPalListKind(X) → isPalListKind(X)
a__U92(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__isQid(X) → isQid(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)
a__isQid(u) → tt
a__isQid(o) → tt
a__isQid(i) → tt
a__isQid(e) → tt
a__isQid(a) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt

(12) Obligation:

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

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)

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

(13) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(14) TRUE

(15) Obligation:

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

A__U12(tt, V) → A__ISNELIST(V)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
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__ISNELIST(V2)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
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__ISLIST(V2)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
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__ISLIST(V2)
A__U24(tt, V1, V2) → A__ISLIST(V1)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U44(tt, V1, V2) → A__ISLIST(V1)

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.

(16) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
A__U44(tt, V1, V2) → A__U45(a__isList(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__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), 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__U24(tt, V1, V2) → A__ISLIST(V1)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U44(tt, V1, V2) → A__ISLIST(V1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A__U12(x1, x2)  =  x2
tt  =  tt
A__ISNELIST(x1)  =  x1
__(x1, x2)  =  __(x1, x2)
A__U41(x1, x2, x3)  =  A__U41(x2, x3)
a__isPalListKind(x1)  =  x1
A__U42(x1, x2, x3)  =  A__U42(x2, x3)
A__U43(x1, x2, x3)  =  A__U43(x2, x3)
A__U44(x1, x2, x3)  =  A__U44(x2, x3)
A__U45(x1, x2)  =  x2
a__isList(x1)  =  a__isList
A__U51(x1, x2, x3)  =  A__U51(x2, x3)
A__U52(x1, x2, x3)  =  A__U52(x2, x3)
A__U53(x1, x2, x3)  =  A__U53(x1, x2, x3)
A__U54(x1, x2, x3)  =  A__U54(x2, x3)
A__U55(x1, x2)  =  A__U55(x2)
a__isNeList(x1)  =  a__isNeList
A__ISLIST(x1)  =  A__ISLIST(x1)
A__U11(x1, x2)  =  x2
A__U21(x1, x2, x3)  =  A__U21(x2, x3)
A__U22(x1, x2, x3)  =  A__U22(x2, x3)
A__U23(x1, x2, x3)  =  A__U23(x2, x3)
A__U24(x1, x2, x3)  =  A__U24(x2, x3)
A__U25(x1, x2)  =  A__U25(x2)
nil  =  nil
o  =  o
e  =  e
i  =  i
a  =  a
a__U51(x1, x2, x3)  =  a__U51(x1)
a__U31(x1, x2)  =  a__U31
a__U41(x1, x2, x3)  =  a__U41(x1, x3)
a__U21(x1, x2, x3)  =  a__U21(x1)
a__U92(x1)  =  a__U92
a__U11(x1, x2)  =  x1
a__isQid(x1)  =  a__isQid(x1)
u  =  u
a__U91(x1, x2)  =  a__U91(x1, x2)
a__U56(x1)  =  a__U56
U56(x1)  =  U56(x1)
a__U44(x1, x2, x3)  =  x3
a__U45(x1, x2)  =  x1
a__U55(x1, x2)  =  a__U55(x1)
U55(x1, x2)  =  U55(x1, x2)
a__U46(x1)  =  a__U46
a__U52(x1, x2, x3)  =  a__U52(x1, x2, x3)
a__U33(x1)  =  a__U33(x1)
U52(x1, x2, x3)  =  U52(x1, x3)
a__U42(x1, x2, x3)  =  a__U42(x1, x2)
U51(x1, x2, x3)  =  x2
a__U54(x1, x2, x3)  =  a__U54(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x3)
a__U43(x1, x2, x3)  =  a__U43(x1, x2)
a__U53(x1, x2, x3)  =  a__U53
U53(x1, x2, x3)  =  U53(x1, x2, x3)
a__U25(x1, x2)  =  x1
a__U26(x1)  =  a__U26
a__U32(x1, x2)  =  a__U32(x1, x2)
a__U22(x1, x2, x3)  =  a__U22(x2, x3)
a__U23(x1, x2, x3)  =  a__U23(x2)
a__U24(x1, x2, x3)  =  x3
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92
U11(x1, x2)  =  U11(x1, x2)
a__U12(x1, x2)  =  a__U12(x2)
U12(x1, x2)  =  U12(x1, x2)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x2)
isPalListKind(x1)  =  x1
a__U13(x1)  =  a__U13
U13(x1)  =  U13(x1)
U42(x1, x2, x3)  =  U42(x1, x3)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
isQid(x1)  =  isQid
U33(x1)  =  U33
U46(x1)  =  U46(x1)
U45(x1, x2)  =  U45
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x3)
U25(x1, x2)  =  U25(x1, x2)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x3)
U22(x1, x2, x3)  =  x1
U32(x1, x2)  =  U32(x1, x2)
U31(x1, x2)  =  U31(x1, x2)
U26(x1)  =  U26(x1)
isList(x1)  =  isList

Lexicographic Path Order [LPO].
Precedence:

[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > [A_U432, A_U442] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > [A_U432, A_U442] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > [A_U432, A_U442] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > [A_U432, A_U442] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > [A_U432, A_U442] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U533 > A_U542 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U533 > A_U542 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U533 > A_U542 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U533 > A_U542 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U533 > A_U542 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U242 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U242 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U242 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U242 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > A_U242 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U412 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U92 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U92 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U92 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U92 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U92 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
[₂, A_U412, A_U422, A_U512, A_U522, A_U212, A_U222, A_U232, a_U912, U91₂] > a_U92 > U92 > U56₁
a_isList > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
a_isList > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
a_isList > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
a_isList > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
a_isList > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
nil > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
nil > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
nil > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
nil > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
nil > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
i > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
i > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
i > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
i > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
i > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
a > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
a > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
a > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
a > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
a > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
a_U211 > a_U222 > U56₁
a_U211 > U21₁ > U56₁
a_isQid1 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
a_isQid1 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
a_isQid1 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
a_isQid1 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
a_isQid1 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
a_isQid1 > isQid > U56₁
U55₂ > U56₁
a_U46 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
a_U46 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
a_U46 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
a_U46 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
a_U46 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
a_U46 > U46₁ > U56₁
U52₂ > U56₁
U54₁ > U56₁
a_U26 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
a_U26 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
a_U26 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
a_U26 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
a_U26 > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
a_U26 > U26₁ > U56₁
a_U231 > U23₁ > U56₁
U11₂ > U56₁
a_U121 > [a_isNeList, a_U511] > a_U31 > a_U322 > a_U331 > U56₁
a_U121 > [a_isNeList, a_U511] > a_U31 > a_U322 > U32₂ > U56₁
a_U121 > [a_isNeList, a_U511] > a_U31 > U31₂ > U56₁
a_U121 > [a_isNeList, a_U511] > a_U412 > U56₁
a_U121 > [a_isNeList, a_U511] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
a_U121 > [a_isNeList, a_U511] > a_U523 > a_U53 > U53₃ > U56₁
U12₂ > U56₁
isNeList₁ > U56₁
[a_U13, U13₁] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > [a_U551, a_U543] > a_U56 > U56₁
[a_U13, U13₁] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U523 > a_U53 > U53₃ > U56₁
[a_U13, U13₁] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > [a_U422, a_U432, U43₁] > U42₂ > U56₁
[a_U13, U13₁] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > a_U331 > U56₁
[a_U13, U13₁] > [tt, A_U551, A_ISLIST1, A_U251, o, e, u] > a_U322 > U32₂ > U56₁
U41₃ > U56₁
U33 > U56₁
U45 > U56₁
U44₃ > U56₁
U25₂ > U56₁
U24₃ > U56₁
isList > U56₁

The following usable rules [FROCOS05] were oriented:

a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(a) → tt
a__U92(tt) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)
a__isPalListKind(X) → isPalListKind(X)

(17) Obligation:

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

A__U12(tt, V) → A__ISNELIST(V)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
A__U45(tt, V2) → A__ISNELIST(V2)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__U55(tt, V2) → A__ISLIST(V2)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
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__U25(tt, V2) → 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.

(18) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 12 less nodes.

(19) TRUE

(20) Obligation:

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

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

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.

(21) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

A____(__(X, Y), Z) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)

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

Lexicographic Path Order [LPO].
Precedence:

[A₂, ₂, a₂] > [U71₂, U72₂, a_U712, a_U722] > [U73₁, a_U731] > [a_{isPalListKind}, tt, e, a_isQid, a_isNeList, a_isList, isNeList, isPalListKind, u, isQid, isList]
[A₂, ₂, a₂] > [U71₂, U72₂, a_U712, a_U722] > [a_isPal1, isPal₁] > [U81₂, U82₂, a_U812, a_U822] > [U83₁, a_U831] > [a_{isPalListKind}, tt, e, a_isQid, a_isNeList, a_isList, isNeList, isPalListKind, u, isQid, isList]
nil > [a_{isPalListKind}, tt, e, a_isQid, a_isNeList, a_isList, isNeList, isPalListKind, u, isQid, isList]
o > [a_{isPalListKind}, tt, e, a_isQid, a_isNeList, a_isList, isNeList, isPalListKind, u, isQid, isList]
i > [a_{isPalListKind}, tt, e, a_isQid, a_isNeList, a_isList, isNeList, isPalListKind, u, isQid, isList]
a > [a_{isPalListKind}, tt, e, a_isQid, a_isNeList, a_isList, isNeList, isPalListKind, u, isQid, isList]

The following usable rules [FROCOS05] were oriented:

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__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U13(X)) → a__U13(mark(X))
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
a__isQid(u) → tt
a__isQid(o) → tt
a__isQid(i) → tt
a__isQid(e) → tt
a__isQid(a) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt
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__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__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__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__U82(tt, V) → a__U83(a__isNePal(V))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U83(tt) → tt
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U74(tt) → tt
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U56(tt) → tt
a__U63(tt) → tt
a__U62(tt, V) → a__U63(a__isQid(V))
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
mark(nil) → nil
mark(tt) → tt
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(i) → i
mark(o) → o
mark(a) → a
mark(e) → e
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__isQid(X) → isQid(X)
a__U33(X) → U33(X)
a__U46(X) → U46(X)
a__U45(X1, X2) → U45(X1, X2)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U32(X1, X2) → U32(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U26(X) → U26(X)
a__isList(X) → isList(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(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(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U74(X)) → a__U74(mark(X))
mark(isPal(X)) → a__isPal(X)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(isNePal(X)) → a__isNePal(X)
mark(U83(X)) → a__U83(mark(X))
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U56(X)) → a__U56(mark(X))
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U63(X)) → a__U63(mark(X))
a__U56(X) → U56(X)
a__U55(X1, X2) → U55(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U61(X1, X2) → U61(X1, X2)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U74(X) → U74(X)
a__isPal(X) → isPal(X)
a__U82(X1, X2) → U82(X1, X2)
a__U81(X1, X2) → U81(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U73(X1, X2) → U73(X1, X2)
a__U72(X1, X2) → U72(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)
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__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt

(22) Obligation:

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

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

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.

(23) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.

(24) Obligation:

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

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

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.

(25) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U33(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U33(x1)  =  U33(x1)
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(26) Obligation:

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

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

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.

(27) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U41(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(28) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(29) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U42(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(30) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(31) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U44(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(32) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(33) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U46(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(34) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(35) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U51(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(36) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(37) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U26(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(38) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(39) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U62(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(40) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(41) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U25(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  U25(x1, x2)
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(42) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(43) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U24(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  U24(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(44) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(45) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U74(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  U74(x1)
U91(x1, x2)  =  x1
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(46) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

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.

(47) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U91(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U63(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(48) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

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.

(49) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U92(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U63(x1)  =  x1
U92(x1)  =  U92(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(50) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)

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.

(51) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U63(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U63(x1)  =  U63(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(52) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(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.

(53) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U56(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  x1
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  U56(x1)
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(54) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(55) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U13(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U13(x1)  =  U13(x1)
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(56) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(57) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U21(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U21(x1, x2, x3)  =  U21(x1, x3)
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(58) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(59) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U22(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(60) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(61) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U45(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  x1
U11(x1, x2)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(62) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(63) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U12(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U12(x1, x2)  =  U12(x1, x2)
U11(x1, x2)  =  x1
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(64) Obligation:

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

MARK(U11(X1, X2)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(65) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U11(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U11(x1, x2)  =  U11(x1)
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(66) Obligation:

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

MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(67) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U32(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U23(x1, x2, x3)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(68) Obligation:

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

MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(69) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U23(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  x1
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U31(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(70) Obligation:

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

MARK(U31(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U61(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.

(71) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U61(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  x1
U31(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U61(x1, x2)  =  U61(x1, x2)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(72) Obligation:

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

MARK(U31(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(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.

(73) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U53(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  x1
U31(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(74) Obligation:

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

MARK(U31(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(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.

(75) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U54(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U31(x1, x2)  =  x1
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(76) Obligation:

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

MARK(U31(X1, X2)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U55(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.

(77) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U31(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U43(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(78) Obligation:

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

MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U55(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.

(79) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U43(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  x1
U43(x1, x2, x3)  =  U43(x1)
U52(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(80) Obligation:

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

MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U55(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.

(81) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U52(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U55(x1, x2)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(82) Obligation:

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

MARK(U55(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.

(83) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U55(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(84) Obligation:

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.

(85) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(86) TRUE