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