(0) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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:

ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
ACTIVE(__(__(X, Y), Z)) → __1(X, __(Y, Z))
ACTIVE(__(__(X, Y), Z)) → __1(Y, Z)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(U11(tt, V)) → MARK(U12(isPalListKind(V), V))
ACTIVE(U11(tt, V)) → U121(isPalListKind(V), V)
ACTIVE(U11(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U12(tt, V)) → MARK(U13(isNeList(V)))
ACTIVE(U12(tt, V)) → U131(isNeList(V))
ACTIVE(U12(tt, V)) → ISNELIST(V)
ACTIVE(U13(tt)) → MARK(tt)
ACTIVE(U21(tt, V1, V2)) → MARK(U22(isPalListKind(V1), V1, V2))
ACTIVE(U21(tt, V1, V2)) → U221(isPalListKind(V1), V1, V2)
ACTIVE(U21(tt, V1, V2)) → ISPALLISTKIND(V1)
ACTIVE(U22(tt, V1, V2)) → MARK(U23(isPalListKind(V2), V1, V2))
ACTIVE(U22(tt, V1, V2)) → U231(isPalListKind(V2), V1, V2)
ACTIVE(U22(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U23(tt, V1, V2)) → MARK(U24(isPalListKind(V2), V1, V2))
ACTIVE(U23(tt, V1, V2)) → U241(isPalListKind(V2), V1, V2)
ACTIVE(U23(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U24(tt, V1, V2)) → MARK(U25(isList(V1), V2))
ACTIVE(U24(tt, V1, V2)) → U251(isList(V1), V2)
ACTIVE(U24(tt, V1, V2)) → ISLIST(V1)
ACTIVE(U25(tt, V2)) → MARK(U26(isList(V2)))
ACTIVE(U25(tt, V2)) → U261(isList(V2))
ACTIVE(U25(tt, V2)) → ISLIST(V2)
ACTIVE(U26(tt)) → MARK(tt)
ACTIVE(U31(tt, V)) → MARK(U32(isPalListKind(V), V))
ACTIVE(U31(tt, V)) → U321(isPalListKind(V), V)
ACTIVE(U31(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U32(tt, V)) → MARK(U33(isQid(V)))
ACTIVE(U32(tt, V)) → U331(isQid(V))
ACTIVE(U32(tt, V)) → ISQID(V)
ACTIVE(U33(tt)) → MARK(tt)
ACTIVE(U41(tt, V1, V2)) → MARK(U42(isPalListKind(V1), V1, V2))
ACTIVE(U41(tt, V1, V2)) → U421(isPalListKind(V1), V1, V2)
ACTIVE(U41(tt, V1, V2)) → ISPALLISTKIND(V1)
ACTIVE(U42(tt, V1, V2)) → MARK(U43(isPalListKind(V2), V1, V2))
ACTIVE(U42(tt, V1, V2)) → U431(isPalListKind(V2), V1, V2)
ACTIVE(U42(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U43(tt, V1, V2)) → MARK(U44(isPalListKind(V2), V1, V2))
ACTIVE(U43(tt, V1, V2)) → U441(isPalListKind(V2), V1, V2)
ACTIVE(U43(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U44(tt, V1, V2)) → MARK(U45(isList(V1), V2))
ACTIVE(U44(tt, V1, V2)) → U451(isList(V1), V2)
ACTIVE(U44(tt, V1, V2)) → ISLIST(V1)
ACTIVE(U45(tt, V2)) → MARK(U46(isNeList(V2)))
ACTIVE(U45(tt, V2)) → U461(isNeList(V2))
ACTIVE(U45(tt, V2)) → ISNELIST(V2)
ACTIVE(U46(tt)) → MARK(tt)
ACTIVE(U51(tt, V1, V2)) → MARK(U52(isPalListKind(V1), V1, V2))
ACTIVE(U51(tt, V1, V2)) → U521(isPalListKind(V1), V1, V2)
ACTIVE(U51(tt, V1, V2)) → ISPALLISTKIND(V1)
ACTIVE(U52(tt, V1, V2)) → MARK(U53(isPalListKind(V2), V1, V2))
ACTIVE(U52(tt, V1, V2)) → U531(isPalListKind(V2), V1, V2)
ACTIVE(U52(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U53(tt, V1, V2)) → MARK(U54(isPalListKind(V2), V1, V2))
ACTIVE(U53(tt, V1, V2)) → U541(isPalListKind(V2), V1, V2)
ACTIVE(U53(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U54(tt, V1, V2)) → MARK(U55(isNeList(V1), V2))
ACTIVE(U54(tt, V1, V2)) → U551(isNeList(V1), V2)
ACTIVE(U54(tt, V1, V2)) → ISNELIST(V1)
ACTIVE(U55(tt, V2)) → MARK(U56(isList(V2)))
ACTIVE(U55(tt, V2)) → U561(isList(V2))
ACTIVE(U55(tt, V2)) → ISLIST(V2)
ACTIVE(U56(tt)) → MARK(tt)
ACTIVE(U61(tt, V)) → MARK(U62(isPalListKind(V), V))
ACTIVE(U61(tt, V)) → U621(isPalListKind(V), V)
ACTIVE(U61(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U62(tt, V)) → MARK(U63(isQid(V)))
ACTIVE(U62(tt, V)) → U631(isQid(V))
ACTIVE(U62(tt, V)) → ISQID(V)
ACTIVE(U63(tt)) → MARK(tt)
ACTIVE(U71(tt, I, P)) → MARK(U72(isPalListKind(I), P))
ACTIVE(U71(tt, I, P)) → U721(isPalListKind(I), P)
ACTIVE(U71(tt, I, P)) → ISPALLISTKIND(I)
ACTIVE(U72(tt, P)) → MARK(U73(isPal(P), P))
ACTIVE(U72(tt, P)) → U731(isPal(P), P)
ACTIVE(U72(tt, P)) → ISPAL(P)
ACTIVE(U73(tt, P)) → MARK(U74(isPalListKind(P)))
ACTIVE(U73(tt, P)) → U741(isPalListKind(P))
ACTIVE(U73(tt, P)) → ISPALLISTKIND(P)
ACTIVE(U74(tt)) → MARK(tt)
ACTIVE(U81(tt, V)) → MARK(U82(isPalListKind(V), V))
ACTIVE(U81(tt, V)) → U821(isPalListKind(V), V)
ACTIVE(U81(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U82(tt, V)) → MARK(U83(isNePal(V)))
ACTIVE(U82(tt, V)) → U831(isNePal(V))
ACTIVE(U82(tt, V)) → ISNEPAL(V)
ACTIVE(U83(tt)) → MARK(tt)
ACTIVE(U91(tt, V2)) → MARK(U92(isPalListKind(V2)))
ACTIVE(U91(tt, V2)) → U921(isPalListKind(V2))
ACTIVE(U91(tt, V2)) → ISPALLISTKIND(V2)
ACTIVE(U92(tt)) → MARK(tt)
ACTIVE(isList(V)) → MARK(U11(isPalListKind(V), V))
ACTIVE(isList(V)) → U111(isPalListKind(V), V)
ACTIVE(isList(V)) → ISPALLISTKIND(V)
ACTIVE(isList(nil)) → MARK(tt)
ACTIVE(isList(__(V1, V2))) → MARK(U21(isPalListKind(V1), V1, V2))
ACTIVE(isList(__(V1, V2))) → U211(isPalListKind(V1), V1, V2)
ACTIVE(isList(__(V1, V2))) → ISPALLISTKIND(V1)
ACTIVE(isNeList(V)) → MARK(U31(isPalListKind(V), V))
ACTIVE(isNeList(V)) → U311(isPalListKind(V), V)
ACTIVE(isNeList(V)) → ISPALLISTKIND(V)
ACTIVE(isNeList(__(V1, V2))) → MARK(U41(isPalListKind(V1), V1, V2))
ACTIVE(isNeList(__(V1, V2))) → U411(isPalListKind(V1), V1, V2)
ACTIVE(isNeList(__(V1, V2))) → ISPALLISTKIND(V1)
ACTIVE(isNeList(__(V1, V2))) → MARK(U51(isPalListKind(V1), V1, V2))
ACTIVE(isNeList(__(V1, V2))) → U511(isPalListKind(V1), V1, V2)
ACTIVE(isNePal(V)) → MARK(U61(isPalListKind(V), V))
ACTIVE(isNePal(V)) → U611(isPalListKind(V), V)
ACTIVE(isNePal(V)) → ISPALLISTKIND(V)
ACTIVE(isNePal(__(I, __(P, I)))) → MARK(U71(isQid(I), I, P))
ACTIVE(isNePal(__(I, __(P, I)))) → U711(isQid(I), I, P)
ACTIVE(isNePal(__(I, __(P, I)))) → ISQID(I)
ACTIVE(isPal(V)) → MARK(U81(isPalListKind(V), V))
ACTIVE(isPal(V)) → U811(isPalListKind(V), V)
ACTIVE(isPal(V)) → ISPALLISTKIND(V)
ACTIVE(isPal(nil)) → MARK(tt)
ACTIVE(isPalListKind(a)) → MARK(tt)
ACTIVE(isPalListKind(e)) → MARK(tt)
ACTIVE(isPalListKind(i)) → MARK(tt)
ACTIVE(isPalListKind(nil)) → MARK(tt)
ACTIVE(isPalListKind(o)) → MARK(tt)
ACTIVE(isPalListKind(u)) → MARK(tt)
ACTIVE(isPalListKind(__(V1, V2))) → MARK(U91(isPalListKind(V1), V2))
ACTIVE(isPalListKind(__(V1, V2))) → U911(isPalListKind(V1), V2)
ACTIVE(isPalListKind(__(V1, V2))) → ISPALLISTKIND(V1)
ACTIVE(isQid(a)) → MARK(tt)
ACTIVE(isQid(e)) → MARK(tt)
ACTIVE(isQid(i)) → MARK(tt)
ACTIVE(isQid(o)) → MARK(tt)
ACTIVE(isQid(u)) → MARK(tt)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(__(X1, X2)) → __1(mark(X1), mark(X2))
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(nil) → ACTIVE(nil)
MARK(U11(X1, X2)) → ACTIVE(U11(mark(X1), X2))
MARK(U11(X1, X2)) → U111(mark(X1), X2)
MARK(U11(X1, X2)) → MARK(X1)
MARK(tt) → ACTIVE(tt)
MARK(U12(X1, X2)) → ACTIVE(U12(mark(X1), X2))
MARK(U12(X1, X2)) → U121(mark(X1), X2)
MARK(U12(X1, X2)) → MARK(X1)
MARK(isPalListKind(X)) → ACTIVE(isPalListKind(X))
MARK(U13(X)) → ACTIVE(U13(mark(X)))
MARK(U13(X)) → U131(mark(X))
MARK(U13(X)) → MARK(X)
MARK(isNeList(X)) → ACTIVE(isNeList(X))
MARK(U21(X1, X2, X3)) → ACTIVE(U21(mark(X1), X2, X3))
MARK(U21(X1, X2, X3)) → U211(mark(X1), X2, X3)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → ACTIVE(U22(mark(X1), X2, X3))
MARK(U22(X1, X2, X3)) → U221(mark(X1), X2, X3)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → ACTIVE(U23(mark(X1), X2, X3))
MARK(U23(X1, X2, X3)) → U231(mark(X1), X2, X3)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → ACTIVE(U24(mark(X1), X2, X3))
MARK(U24(X1, X2, X3)) → U241(mark(X1), X2, X3)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → ACTIVE(U25(mark(X1), X2))
MARK(U25(X1, X2)) → U251(mark(X1), X2)
MARK(U25(X1, X2)) → MARK(X1)
MARK(isList(X)) → ACTIVE(isList(X))
MARK(U26(X)) → ACTIVE(U26(mark(X)))
MARK(U26(X)) → U261(mark(X))
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
MARK(U31(X1, X2)) → U311(mark(X1), X2)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → ACTIVE(U32(mark(X1), X2))
MARK(U32(X1, X2)) → U321(mark(X1), X2)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → ACTIVE(U33(mark(X)))
MARK(U33(X)) → U331(mark(X))
MARK(U33(X)) → MARK(X)
MARK(isQid(X)) → ACTIVE(isQid(X))
MARK(U41(X1, X2, X3)) → ACTIVE(U41(mark(X1), X2, X3))
MARK(U41(X1, X2, X3)) → U411(mark(X1), X2, X3)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → ACTIVE(U42(mark(X1), X2, X3))
MARK(U42(X1, X2, X3)) → U421(mark(X1), X2, X3)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → ACTIVE(U43(mark(X1), X2, X3))
MARK(U43(X1, X2, X3)) → U431(mark(X1), X2, X3)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → ACTIVE(U44(mark(X1), X2, X3))
MARK(U44(X1, X2, X3)) → U441(mark(X1), X2, X3)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → ACTIVE(U45(mark(X1), X2))
MARK(U45(X1, X2)) → U451(mark(X1), X2)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → ACTIVE(U46(mark(X)))
MARK(U46(X)) → U461(mark(X))
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → ACTIVE(U51(mark(X1), X2, X3))
MARK(U51(X1, X2, X3)) → U511(mark(X1), X2, X3)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → ACTIVE(U52(mark(X1), X2, X3))
MARK(U52(X1, X2, X3)) → U521(mark(X1), X2, X3)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → ACTIVE(U53(mark(X1), X2, X3))
MARK(U53(X1, X2, X3)) → U531(mark(X1), X2, X3)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → ACTIVE(U54(mark(X1), X2, X3))
MARK(U54(X1, X2, X3)) → U541(mark(X1), X2, X3)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → ACTIVE(U55(mark(X1), X2))
MARK(U55(X1, X2)) → U551(mark(X1), X2)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → ACTIVE(U56(mark(X)))
MARK(U56(X)) → U561(mark(X))
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
MARK(U61(X1, X2)) → U611(mark(X1), X2)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → ACTIVE(U62(mark(X1), X2))
MARK(U62(X1, X2)) → U621(mark(X1), X2)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → ACTIVE(U63(mark(X)))
MARK(U63(X)) → U631(mark(X))
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → ACTIVE(U71(mark(X1), X2, X3))
MARK(U71(X1, X2, X3)) → U711(mark(X1), X2, X3)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → ACTIVE(U72(mark(X1), X2))
MARK(U72(X1, X2)) → U721(mark(X1), X2)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → ACTIVE(U73(mark(X1), X2))
MARK(U73(X1, X2)) → U731(mark(X1), X2)
MARK(U73(X1, X2)) → MARK(X1)
MARK(isPal(X)) → ACTIVE(isPal(X))
MARK(U74(X)) → ACTIVE(U74(mark(X)))
MARK(U74(X)) → U741(mark(X))
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → ACTIVE(U81(mark(X1), X2))
MARK(U81(X1, X2)) → U811(mark(X1), X2)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → ACTIVE(U82(mark(X1), X2))
MARK(U82(X1, X2)) → U821(mark(X1), X2)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → ACTIVE(U83(mark(X)))
MARK(U83(X)) → U831(mark(X))
MARK(U83(X)) → MARK(X)
MARK(isNePal(X)) → ACTIVE(isNePal(X))
MARK(U91(X1, X2)) → ACTIVE(U91(mark(X1), X2))
MARK(U91(X1, X2)) → U911(mark(X1), X2)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → ACTIVE(U92(mark(X)))
MARK(U92(X)) → U921(mark(X))
MARK(U92(X)) → MARK(X)
MARK(a) → ACTIVE(a)
MARK(e) → ACTIVE(e)
MARK(i) → ACTIVE(i)
MARK(o) → ACTIVE(o)
MARK(u) → ACTIVE(u)
__1(mark(X1), X2) → __1(X1, X2)
__1(X1, mark(X2)) → __1(X1, X2)
__1(active(X1), X2) → __1(X1, X2)
__1(X1, active(X2)) → __1(X1, X2)
U111(mark(X1), X2) → U111(X1, X2)
U111(X1, mark(X2)) → U111(X1, X2)
U111(active(X1), X2) → U111(X1, X2)
U111(X1, active(X2)) → U111(X1, X2)
U121(mark(X1), X2) → U121(X1, X2)
U121(X1, mark(X2)) → U121(X1, X2)
U121(active(X1), X2) → U121(X1, X2)
U121(X1, active(X2)) → U121(X1, X2)
ISPALLISTKIND(mark(X)) → ISPALLISTKIND(X)
ISPALLISTKIND(active(X)) → ISPALLISTKIND(X)
U131(mark(X)) → U131(X)
U131(active(X)) → U131(X)
ISNELIST(mark(X)) → ISNELIST(X)
ISNELIST(active(X)) → ISNELIST(X)
U211(mark(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, mark(X2), X3) → U211(X1, X2, X3)
U211(X1, X2, mark(X3)) → U211(X1, X2, X3)
U211(active(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, active(X2), X3) → U211(X1, X2, X3)
U211(X1, X2, active(X3)) → U211(X1, X2, X3)
U221(mark(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, mark(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, mark(X3)) → U221(X1, X2, X3)
U221(active(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, active(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, active(X3)) → U221(X1, X2, X3)
U231(mark(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, mark(X2), X3) → U231(X1, X2, X3)
U231(X1, X2, mark(X3)) → U231(X1, X2, X3)
U231(active(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, active(X2), X3) → U231(X1, X2, X3)
U231(X1, X2, active(X3)) → U231(X1, X2, X3)
U241(mark(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, mark(X2), X3) → U241(X1, X2, X3)
U241(X1, X2, mark(X3)) → U241(X1, X2, X3)
U241(active(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, active(X2), X3) → U241(X1, X2, X3)
U241(X1, X2, active(X3)) → U241(X1, X2, X3)
U251(mark(X1), X2) → U251(X1, X2)
U251(X1, mark(X2)) → U251(X1, X2)
U251(active(X1), X2) → U251(X1, X2)
U251(X1, active(X2)) → U251(X1, X2)
ISLIST(mark(X)) → ISLIST(X)
ISLIST(active(X)) → ISLIST(X)
U261(mark(X)) → U261(X)
U261(active(X)) → U261(X)
U311(mark(X1), X2) → U311(X1, X2)
U311(X1, mark(X2)) → U311(X1, X2)
U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)
U321(mark(X1), X2) → U321(X1, X2)
U321(X1, mark(X2)) → U321(X1, X2)
U321(active(X1), X2) → U321(X1, X2)
U321(X1, active(X2)) → U321(X1, X2)
U331(mark(X)) → U331(X)
U331(active(X)) → U331(X)
ISQID(mark(X)) → ISQID(X)
ISQID(active(X)) → ISQID(X)
U411(mark(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, mark(X2), X3) → U411(X1, X2, X3)
U411(X1, X2, mark(X3)) → U411(X1, X2, X3)
U411(active(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, active(X2), X3) → U411(X1, X2, X3)
U411(X1, X2, active(X3)) → U411(X1, X2, X3)
U421(mark(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, mark(X2), X3) → U421(X1, X2, X3)
U421(X1, X2, mark(X3)) → U421(X1, X2, X3)
U421(active(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, active(X2), X3) → U421(X1, X2, X3)
U421(X1, X2, active(X3)) → U421(X1, X2, X3)
U431(mark(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, mark(X2), X3) → U431(X1, X2, X3)
U431(X1, X2, mark(X3)) → U431(X1, X2, X3)
U431(active(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, active(X2), X3) → U431(X1, X2, X3)
U431(X1, X2, active(X3)) → U431(X1, X2, X3)
U441(mark(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, mark(X2), X3) → U441(X1, X2, X3)
U441(X1, X2, mark(X3)) → U441(X1, X2, X3)
U441(active(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, active(X2), X3) → U441(X1, X2, X3)
U441(X1, X2, active(X3)) → U441(X1, X2, X3)
U451(mark(X1), X2) → U451(X1, X2)
U451(X1, mark(X2)) → U451(X1, X2)
U451(active(X1), X2) → U451(X1, X2)
U451(X1, active(X2)) → U451(X1, X2)
U461(mark(X)) → U461(X)
U461(active(X)) → U461(X)
U511(mark(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, mark(X2), X3) → U511(X1, X2, X3)
U511(X1, X2, mark(X3)) → U511(X1, X2, X3)
U511(active(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, active(X2), X3) → U511(X1, X2, X3)
U511(X1, X2, active(X3)) → U511(X1, X2, X3)
U521(mark(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, mark(X2), X3) → U521(X1, X2, X3)
U521(X1, X2, mark(X3)) → U521(X1, X2, X3)
U521(active(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, active(X2), X3) → U521(X1, X2, X3)
U521(X1, X2, active(X3)) → U521(X1, X2, X3)
U531(mark(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, mark(X2), X3) → U531(X1, X2, X3)
U531(X1, X2, mark(X3)) → U531(X1, X2, X3)
U531(active(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, active(X2), X3) → U531(X1, X2, X3)
U531(X1, X2, active(X3)) → U531(X1, X2, X3)
U541(mark(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, mark(X2), X3) → U541(X1, X2, X3)
U541(X1, X2, mark(X3)) → U541(X1, X2, X3)
U541(active(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, active(X2), X3) → U541(X1, X2, X3)
U541(X1, X2, active(X3)) → U541(X1, X2, X3)
U551(mark(X1), X2) → U551(X1, X2)
U551(X1, mark(X2)) → U551(X1, X2)
U551(active(X1), X2) → U551(X1, X2)
U551(X1, active(X2)) → U551(X1, X2)
U561(mark(X)) → U561(X)
U561(active(X)) → U561(X)
U611(mark(X1), X2) → U611(X1, X2)
U611(X1, mark(X2)) → U611(X1, X2)
U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)
U621(mark(X1), X2) → U621(X1, X2)
U621(X1, mark(X2)) → U621(X1, X2)
U621(active(X1), X2) → U621(X1, X2)
U621(X1, active(X2)) → U621(X1, X2)
U631(mark(X)) → U631(X)
U631(active(X)) → U631(X)
U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, mark(X3)) → U711(X1, X2, X3)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)
U721(mark(X1), X2) → U721(X1, X2)
U721(X1, mark(X2)) → U721(X1, X2)
U721(active(X1), X2) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)
U731(mark(X1), X2) → U731(X1, X2)
U731(X1, mark(X2)) → U731(X1, X2)
U731(active(X1), X2) → U731(X1, X2)
U731(X1, active(X2)) → U731(X1, X2)
ISPAL(mark(X)) → ISPAL(X)
ISPAL(active(X)) → ISPAL(X)
U741(mark(X)) → U741(X)
U741(active(X)) → U741(X)
U811(mark(X1), X2) → U811(X1, X2)
U811(X1, mark(X2)) → U811(X1, X2)
U811(active(X1), X2) → U811(X1, X2)
U811(X1, active(X2)) → U811(X1, X2)
U821(mark(X1), X2) → U821(X1, X2)
U821(X1, mark(X2)) → U821(X1, X2)
U821(active(X1), X2) → U821(X1, X2)
U821(X1, active(X2)) → U821(X1, X2)
U831(mark(X)) → U831(X)
U831(active(X)) → U831(X)
ISNEPAL(mark(X)) → ISNEPAL(X)
ISNEPAL(active(X)) → ISNEPAL(X)
U911(mark(X1), X2) → U911(X1, X2)
U911(X1, mark(X2)) → U911(X1, X2)
U911(active(X1), X2) → U911(X1, X2)
U911(X1, active(X2)) → U911(X1, X2)
U921(mark(X)) → U921(X)
U921(active(X)) → U921(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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 44 SCCs with 139 less nodes.

(4) Complex Obligation (AND)

(5) Obligation:

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

U921(active(X)) → U921(X)
U921(mark(X)) → U921(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U921(active(X)) → U921(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U921(x1)  =  U921(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U92^11

The following usable rules [FROCOS05] were oriented: none

(7) Obligation:

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

U921(mark(X)) → U921(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(8) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U921(mark(X)) → U921(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U92^11

The following usable rules [FROCOS05] were oriented: none

(9) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(10) PisEmptyProof (EQUIVALENT transformation)

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

(11) TRUE

(12) Obligation:

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

U911(X1, mark(X2)) → U911(X1, X2)
U911(mark(X1), X2) → U911(X1, X2)
U911(active(X1), X2) → U911(X1, X2)
U911(X1, active(X2)) → U911(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(13) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U911(X1, mark(X2)) → U911(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U911(x1, x2)  =  U911(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U91^11

The following usable rules [FROCOS05] were oriented: none

(14) Obligation:

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

U911(mark(X1), X2) → U911(X1, X2)
U911(active(X1), X2) → U911(X1, X2)
U911(X1, active(X2)) → U911(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(15) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U911(mark(X1), X2) → U911(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U911(x1, x2)  =  U911(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U91^12

The following usable rules [FROCOS05] were oriented: none

(16) Obligation:

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

U911(active(X1), X2) → U911(X1, X2)
U911(X1, active(X2)) → U911(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(17) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U911(active(X1), X2) → U911(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U911(x1, x2)  =  U911(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U91^11

The following usable rules [FROCOS05] were oriented: none

(18) Obligation:

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

U911(X1, active(X2)) → U911(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(19) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U911(X1, active(X2)) → U911(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U911(x1, x2)  =  U911(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U91^11

The following usable rules [FROCOS05] were oriented: none

(20) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(21) PisEmptyProof (EQUIVALENT transformation)

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

(22) TRUE

(23) Obligation:

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

ISNEPAL(active(X)) → ISNEPAL(X)
ISNEPAL(mark(X)) → ISNEPAL(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(24) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISNEPAL(active(X)) → ISNEPAL(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ISNEPAL(x1)  =  ISNEPAL(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > ISNEPAL1

The following usable rules [FROCOS05] were oriented: none

(25) Obligation:

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

ISNEPAL(mark(X)) → ISNEPAL(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(26) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISNEPAL(mark(X)) → ISNEPAL(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > ISNEPAL1

The following usable rules [FROCOS05] were oriented: none

(27) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(28) PisEmptyProof (EQUIVALENT transformation)

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

(29) TRUE

(30) Obligation:

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

U831(active(X)) → U831(X)
U831(mark(X)) → U831(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U831(active(X)) → U831(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U831(x1)  =  U831(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U83^11

The following usable rules [FROCOS05] were oriented: none

(32) Obligation:

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

U831(mark(X)) → U831(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U831(mark(X)) → U831(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U83^11

The following usable rules [FROCOS05] were oriented: none

(34) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(35) PisEmptyProof (EQUIVALENT transformation)

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

(36) TRUE

(37) Obligation:

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

U821(X1, mark(X2)) → U821(X1, X2)
U821(mark(X1), X2) → U821(X1, X2)
U821(active(X1), X2) → U821(X1, X2)
U821(X1, active(X2)) → U821(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(38) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U821(X1, mark(X2)) → U821(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U821(x1, x2)  =  U821(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U82^11

The following usable rules [FROCOS05] were oriented: none

(39) Obligation:

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

U821(mark(X1), X2) → U821(X1, X2)
U821(active(X1), X2) → U821(X1, X2)
U821(X1, active(X2)) → U821(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(40) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U821(mark(X1), X2) → U821(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U821(x1, x2)  =  U821(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U82^12

The following usable rules [FROCOS05] were oriented: none

(41) Obligation:

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

U821(active(X1), X2) → U821(X1, X2)
U821(X1, active(X2)) → U821(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(42) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U821(active(X1), X2) → U821(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U821(x1, x2)  =  U821(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U82^11

The following usable rules [FROCOS05] were oriented: none

(43) Obligation:

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

U821(X1, active(X2)) → U821(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(44) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U821(X1, active(X2)) → U821(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U821(x1, x2)  =  U821(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U82^11

The following usable rules [FROCOS05] were oriented: none

(45) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(46) PisEmptyProof (EQUIVALENT transformation)

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

(47) TRUE

(48) Obligation:

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

U811(X1, mark(X2)) → U811(X1, X2)
U811(mark(X1), X2) → U811(X1, X2)
U811(active(X1), X2) → U811(X1, X2)
U811(X1, active(X2)) → U811(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U811(X1, mark(X2)) → U811(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U811(x1, x2)  =  U811(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U81^11

The following usable rules [FROCOS05] were oriented: none

(50) Obligation:

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

U811(mark(X1), X2) → U811(X1, X2)
U811(active(X1), X2) → U811(X1, X2)
U811(X1, active(X2)) → U811(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U811(mark(X1), X2) → U811(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U811(x1, x2)  =  U811(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U81^12

The following usable rules [FROCOS05] were oriented: none

(52) Obligation:

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

U811(active(X1), X2) → U811(X1, X2)
U811(X1, active(X2)) → U811(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U811(active(X1), X2) → U811(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U811(x1, x2)  =  U811(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U81^11

The following usable rules [FROCOS05] were oriented: none

(54) Obligation:

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

U811(X1, active(X2)) → U811(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


U811(X1, active(X2)) → U811(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U811(x1, x2)  =  U811(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U81^11

The following usable rules [FROCOS05] were oriented: none

(56) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(57) PisEmptyProof (EQUIVALENT transformation)

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

(58) TRUE

(59) Obligation:

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

U741(active(X)) → U741(X)
U741(mark(X)) → U741(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(60) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U741(active(X)) → U741(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U741(x1)  =  U741(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U74^11

The following usable rules [FROCOS05] were oriented: none

(61) Obligation:

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

U741(mark(X)) → U741(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(62) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U741(mark(X)) → U741(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U74^11

The following usable rules [FROCOS05] were oriented: none

(63) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(64) PisEmptyProof (EQUIVALENT transformation)

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

(65) TRUE

(66) Obligation:

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

ISPAL(active(X)) → ISPAL(X)
ISPAL(mark(X)) → ISPAL(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


ISPAL(active(X)) → ISPAL(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ISPAL(x1)  =  ISPAL(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > ISPAL1

The following usable rules [FROCOS05] were oriented: none

(68) Obligation:

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

ISPAL(mark(X)) → ISPAL(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(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.


ISPAL(mark(X)) → ISPAL(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > ISPAL1

The following usable rules [FROCOS05] were oriented: none

(70) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(71) PisEmptyProof (EQUIVALENT transformation)

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

(72) TRUE

(73) Obligation:

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

U731(X1, mark(X2)) → U731(X1, X2)
U731(mark(X1), X2) → U731(X1, X2)
U731(active(X1), X2) → U731(X1, X2)
U731(X1, active(X2)) → U731(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(74) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U731(X1, mark(X2)) → U731(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U731(x1, x2)  =  U731(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U73^11

The following usable rules [FROCOS05] were oriented: none

(75) Obligation:

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

U731(mark(X1), X2) → U731(X1, X2)
U731(active(X1), X2) → U731(X1, X2)
U731(X1, active(X2)) → U731(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(76) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U731(mark(X1), X2) → U731(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U731(x1, x2)  =  U731(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U73^12

The following usable rules [FROCOS05] were oriented: none

(77) Obligation:

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

U731(active(X1), X2) → U731(X1, X2)
U731(X1, active(X2)) → U731(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(78) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U731(active(X1), X2) → U731(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U731(x1, x2)  =  U731(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U73^11

The following usable rules [FROCOS05] were oriented: none

(79) Obligation:

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

U731(X1, active(X2)) → U731(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(80) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U731(X1, active(X2)) → U731(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U731(x1, x2)  =  U731(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U73^11

The following usable rules [FROCOS05] were oriented: none

(81) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(82) PisEmptyProof (EQUIVALENT transformation)

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

(83) TRUE

(84) Obligation:

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

U721(X1, mark(X2)) → U721(X1, X2)
U721(mark(X1), X2) → U721(X1, X2)
U721(active(X1), X2) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(85) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U721(X1, mark(X2)) → U721(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U721(x1, x2)  =  U721(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U72^11

The following usable rules [FROCOS05] were oriented: none

(86) Obligation:

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

U721(mark(X1), X2) → U721(X1, X2)
U721(active(X1), X2) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(87) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U721(mark(X1), X2) → U721(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U721(x1, x2)  =  U721(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U72^12

The following usable rules [FROCOS05] were oriented: none

(88) Obligation:

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

U721(active(X1), X2) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(89) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U721(active(X1), X2) → U721(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U721(x1, x2)  =  U721(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U72^11

The following usable rules [FROCOS05] were oriented: none

(90) Obligation:

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

U721(X1, active(X2)) → U721(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(91) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U721(X1, active(X2)) → U721(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U721(x1, x2)  =  U721(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U72^11

The following usable rules [FROCOS05] were oriented: none

(92) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(93) PisEmptyProof (EQUIVALENT transformation)

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

(94) TRUE

(95) Obligation:

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

U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, X2, mark(X3)) → U711(X1, X2, X3)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(96) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, X2, mark(X3)) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  U711(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(97) Obligation:

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

U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(98) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(X1, mark(X2), X3) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  U711(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(99) Obligation:

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

U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(100) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(active(X1), X2, X3) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  U711(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U71^11

The following usable rules [FROCOS05] were oriented: none

(101) Obligation:

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

U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(102) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(X1, active(X2), X3) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  U711(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U71^11

The following usable rules [FROCOS05] were oriented: none

(103) Obligation:

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

U711(X1, X2, active(X3)) → U711(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(104) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(X1, X2, active(X3)) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  U711(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U71^11

The following usable rules [FROCOS05] were oriented: none

(105) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(106) PisEmptyProof (EQUIVALENT transformation)

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

(107) TRUE

(108) Obligation:

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

U631(active(X)) → U631(X)
U631(mark(X)) → U631(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(109) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U631(active(X)) → U631(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U631(x1)  =  U631(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U63^11

The following usable rules [FROCOS05] were oriented: none

(110) Obligation:

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

U631(mark(X)) → U631(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(111) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U631(mark(X)) → U631(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U63^11

The following usable rules [FROCOS05] were oriented: none

(112) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(113) PisEmptyProof (EQUIVALENT transformation)

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

(114) TRUE

(115) Obligation:

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

U621(X1, mark(X2)) → U621(X1, X2)
U621(mark(X1), X2) → U621(X1, X2)
U621(active(X1), X2) → U621(X1, X2)
U621(X1, active(X2)) → U621(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(116) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U621(X1, mark(X2)) → U621(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U621(x1, x2)  =  U621(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U62^11

The following usable rules [FROCOS05] were oriented: none

(117) Obligation:

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

U621(mark(X1), X2) → U621(X1, X2)
U621(active(X1), X2) → U621(X1, X2)
U621(X1, active(X2)) → U621(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(118) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U621(mark(X1), X2) → U621(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U621(x1, x2)  =  U621(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U62^12

The following usable rules [FROCOS05] were oriented: none

(119) Obligation:

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

U621(active(X1), X2) → U621(X1, X2)
U621(X1, active(X2)) → U621(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(120) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U621(active(X1), X2) → U621(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U621(x1, x2)  =  U621(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U62^11

The following usable rules [FROCOS05] were oriented: none

(121) Obligation:

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

U621(X1, active(X2)) → U621(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(122) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U621(X1, active(X2)) → U621(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U621(x1, x2)  =  U621(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U62^11

The following usable rules [FROCOS05] were oriented: none

(123) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(124) PisEmptyProof (EQUIVALENT transformation)

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

(125) TRUE

(126) Obligation:

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

U611(X1, mark(X2)) → U611(X1, X2)
U611(mark(X1), X2) → U611(X1, X2)
U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(127) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U611(X1, mark(X2)) → U611(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U611(x1, x2)  =  U611(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U61^11

The following usable rules [FROCOS05] were oriented: none

(128) Obligation:

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

U611(mark(X1), X2) → U611(X1, X2)
U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(129) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U611(mark(X1), X2) → U611(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U611(x1, x2)  =  U611(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U61^12

The following usable rules [FROCOS05] were oriented: none

(130) Obligation:

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

U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(131) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U611(active(X1), X2) → U611(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U611(x1, x2)  =  U611(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U61^11

The following usable rules [FROCOS05] were oriented: none

(132) Obligation:

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

U611(X1, active(X2)) → U611(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(133) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U611(X1, active(X2)) → U611(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U611(x1, x2)  =  U611(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U61^11

The following usable rules [FROCOS05] were oriented: none

(134) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(135) PisEmptyProof (EQUIVALENT transformation)

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

(136) TRUE

(137) Obligation:

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

U561(active(X)) → U561(X)
U561(mark(X)) → U561(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(138) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U561(active(X)) → U561(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U561(x1)  =  U561(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U56^11

The following usable rules [FROCOS05] were oriented: none

(139) Obligation:

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

U561(mark(X)) → U561(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(140) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U561(mark(X)) → U561(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U56^11

The following usable rules [FROCOS05] were oriented: none

(141) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(142) PisEmptyProof (EQUIVALENT transformation)

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

(143) TRUE

(144) Obligation:

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

U551(X1, mark(X2)) → U551(X1, X2)
U551(mark(X1), X2) → U551(X1, X2)
U551(active(X1), X2) → U551(X1, X2)
U551(X1, active(X2)) → U551(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(145) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U551(X1, mark(X2)) → U551(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U551(x1, x2)  =  U551(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U55^11

The following usable rules [FROCOS05] were oriented: none

(146) Obligation:

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

U551(mark(X1), X2) → U551(X1, X2)
U551(active(X1), X2) → U551(X1, X2)
U551(X1, active(X2)) → U551(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(147) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U551(mark(X1), X2) → U551(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U551(x1, x2)  =  U551(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U55^12

The following usable rules [FROCOS05] were oriented: none

(148) Obligation:

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

U551(active(X1), X2) → U551(X1, X2)
U551(X1, active(X2)) → U551(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(149) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U551(active(X1), X2) → U551(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U551(x1, x2)  =  U551(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U55^11

The following usable rules [FROCOS05] were oriented: none

(150) Obligation:

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

U551(X1, active(X2)) → U551(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(151) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U551(X1, active(X2)) → U551(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U551(x1, x2)  =  U551(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U55^11

The following usable rules [FROCOS05] were oriented: none

(152) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(153) PisEmptyProof (EQUIVALENT transformation)

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

(154) TRUE

(155) Obligation:

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

U541(X1, mark(X2), X3) → U541(X1, X2, X3)
U541(mark(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, X2, mark(X3)) → U541(X1, X2, X3)
U541(active(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, active(X2), X3) → U541(X1, X2, X3)
U541(X1, X2, active(X3)) → U541(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(156) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(mark(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, X2, mark(X3)) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  U541(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(157) Obligation:

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

U541(X1, mark(X2), X3) → U541(X1, X2, X3)
U541(active(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, active(X2), X3) → U541(X1, X2, X3)
U541(X1, X2, active(X3)) → U541(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(158) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(X1, mark(X2), X3) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  U541(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(159) Obligation:

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

U541(active(X1), X2, X3) → U541(X1, X2, X3)
U541(X1, active(X2), X3) → U541(X1, X2, X3)
U541(X1, X2, active(X3)) → U541(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(160) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(active(X1), X2, X3) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  U541(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U54^11

The following usable rules [FROCOS05] were oriented: none

(161) Obligation:

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

U541(X1, active(X2), X3) → U541(X1, X2, X3)
U541(X1, X2, active(X3)) → U541(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(162) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(X1, active(X2), X3) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  U541(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U54^11

The following usable rules [FROCOS05] were oriented: none

(163) Obligation:

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

U541(X1, X2, active(X3)) → U541(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(164) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(X1, X2, active(X3)) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  U541(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U54^11

The following usable rules [FROCOS05] were oriented: none

(165) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(166) PisEmptyProof (EQUIVALENT transformation)

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

(167) TRUE

(168) Obligation:

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

U531(X1, mark(X2), X3) → U531(X1, X2, X3)
U531(mark(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, X2, mark(X3)) → U531(X1, X2, X3)
U531(active(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, active(X2), X3) → U531(X1, X2, X3)
U531(X1, X2, active(X3)) → U531(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(169) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(mark(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, X2, mark(X3)) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  U531(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(170) Obligation:

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

U531(X1, mark(X2), X3) → U531(X1, X2, X3)
U531(active(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, active(X2), X3) → U531(X1, X2, X3)
U531(X1, X2, active(X3)) → U531(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(171) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(X1, mark(X2), X3) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  U531(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(172) Obligation:

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

U531(active(X1), X2, X3) → U531(X1, X2, X3)
U531(X1, active(X2), X3) → U531(X1, X2, X3)
U531(X1, X2, active(X3)) → U531(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(173) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(active(X1), X2, X3) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  U531(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U53^11

The following usable rules [FROCOS05] were oriented: none

(174) Obligation:

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

U531(X1, active(X2), X3) → U531(X1, X2, X3)
U531(X1, X2, active(X3)) → U531(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(175) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(X1, active(X2), X3) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  U531(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U53^11

The following usable rules [FROCOS05] were oriented: none

(176) Obligation:

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

U531(X1, X2, active(X3)) → U531(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(177) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(X1, X2, active(X3)) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  U531(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U53^11

The following usable rules [FROCOS05] were oriented: none

(178) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(179) PisEmptyProof (EQUIVALENT transformation)

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

(180) TRUE

(181) Obligation:

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

U521(X1, mark(X2), X3) → U521(X1, X2, X3)
U521(mark(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, X2, mark(X3)) → U521(X1, X2, X3)
U521(active(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, active(X2), X3) → U521(X1, X2, X3)
U521(X1, X2, active(X3)) → U521(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(182) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(mark(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, X2, mark(X3)) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  U521(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(183) Obligation:

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

U521(X1, mark(X2), X3) → U521(X1, X2, X3)
U521(active(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, active(X2), X3) → U521(X1, X2, X3)
U521(X1, X2, active(X3)) → U521(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(184) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(X1, mark(X2), X3) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  U521(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(185) Obligation:

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

U521(active(X1), X2, X3) → U521(X1, X2, X3)
U521(X1, active(X2), X3) → U521(X1, X2, X3)
U521(X1, X2, active(X3)) → U521(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(186) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(active(X1), X2, X3) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  U521(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U52^11

The following usable rules [FROCOS05] were oriented: none

(187) Obligation:

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

U521(X1, active(X2), X3) → U521(X1, X2, X3)
U521(X1, X2, active(X3)) → U521(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(188) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(X1, active(X2), X3) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  U521(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U52^11

The following usable rules [FROCOS05] were oriented: none

(189) Obligation:

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

U521(X1, X2, active(X3)) → U521(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(190) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(X1, X2, active(X3)) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  U521(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U52^11

The following usable rules [FROCOS05] were oriented: none

(191) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(192) PisEmptyProof (EQUIVALENT transformation)

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

(193) TRUE

(194) Obligation:

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

U511(X1, mark(X2), X3) → U511(X1, X2, X3)
U511(mark(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, X2, mark(X3)) → U511(X1, X2, X3)
U511(active(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, active(X2), X3) → U511(X1, X2, X3)
U511(X1, X2, active(X3)) → U511(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(195) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(mark(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, X2, mark(X3)) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  U511(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(196) Obligation:

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

U511(X1, mark(X2), X3) → U511(X1, X2, X3)
U511(active(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, active(X2), X3) → U511(X1, X2, X3)
U511(X1, X2, active(X3)) → U511(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(197) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(X1, mark(X2), X3) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  U511(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(198) Obligation:

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

U511(active(X1), X2, X3) → U511(X1, X2, X3)
U511(X1, active(X2), X3) → U511(X1, X2, X3)
U511(X1, X2, active(X3)) → U511(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(199) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(active(X1), X2, X3) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  U511(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U51^11

The following usable rules [FROCOS05] were oriented: none

(200) Obligation:

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

U511(X1, active(X2), X3) → U511(X1, X2, X3)
U511(X1, X2, active(X3)) → U511(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(201) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(X1, active(X2), X3) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  U511(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U51^11

The following usable rules [FROCOS05] were oriented: none

(202) Obligation:

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

U511(X1, X2, active(X3)) → U511(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(203) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(X1, X2, active(X3)) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  U511(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U51^11

The following usable rules [FROCOS05] were oriented: none

(204) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(205) PisEmptyProof (EQUIVALENT transformation)

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

(206) TRUE

(207) Obligation:

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

U461(active(X)) → U461(X)
U461(mark(X)) → U461(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(208) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U461(active(X)) → U461(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U461(x1)  =  U461(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U46^11

The following usable rules [FROCOS05] were oriented: none

(209) Obligation:

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

U461(mark(X)) → U461(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(210) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U461(mark(X)) → U461(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U46^11

The following usable rules [FROCOS05] were oriented: none

(211) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(212) PisEmptyProof (EQUIVALENT transformation)

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

(213) TRUE

(214) Obligation:

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

U451(X1, mark(X2)) → U451(X1, X2)
U451(mark(X1), X2) → U451(X1, X2)
U451(active(X1), X2) → U451(X1, X2)
U451(X1, active(X2)) → U451(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(215) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U451(X1, mark(X2)) → U451(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U451(x1, x2)  =  U451(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U45^11

The following usable rules [FROCOS05] were oriented: none

(216) Obligation:

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

U451(mark(X1), X2) → U451(X1, X2)
U451(active(X1), X2) → U451(X1, X2)
U451(X1, active(X2)) → U451(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(217) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U451(mark(X1), X2) → U451(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U451(x1, x2)  =  U451(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U45^12

The following usable rules [FROCOS05] were oriented: none

(218) Obligation:

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

U451(active(X1), X2) → U451(X1, X2)
U451(X1, active(X2)) → U451(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(219) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U451(active(X1), X2) → U451(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U451(x1, x2)  =  U451(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U45^11

The following usable rules [FROCOS05] were oriented: none

(220) Obligation:

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

U451(X1, active(X2)) → U451(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(221) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U451(X1, active(X2)) → U451(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U451(x1, x2)  =  U451(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U45^11

The following usable rules [FROCOS05] were oriented: none

(222) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(223) PisEmptyProof (EQUIVALENT transformation)

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

(224) TRUE

(225) Obligation:

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

U441(X1, mark(X2), X3) → U441(X1, X2, X3)
U441(mark(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, X2, mark(X3)) → U441(X1, X2, X3)
U441(active(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, active(X2), X3) → U441(X1, X2, X3)
U441(X1, X2, active(X3)) → U441(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(226) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(mark(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, X2, mark(X3)) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  U441(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(227) Obligation:

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

U441(X1, mark(X2), X3) → U441(X1, X2, X3)
U441(active(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, active(X2), X3) → U441(X1, X2, X3)
U441(X1, X2, active(X3)) → U441(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(228) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(X1, mark(X2), X3) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  U441(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(229) Obligation:

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

U441(active(X1), X2, X3) → U441(X1, X2, X3)
U441(X1, active(X2), X3) → U441(X1, X2, X3)
U441(X1, X2, active(X3)) → U441(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(230) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(active(X1), X2, X3) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  U441(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U44^11

The following usable rules [FROCOS05] were oriented: none

(231) Obligation:

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

U441(X1, active(X2), X3) → U441(X1, X2, X3)
U441(X1, X2, active(X3)) → U441(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(232) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(X1, active(X2), X3) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  U441(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U44^11

The following usable rules [FROCOS05] were oriented: none

(233) Obligation:

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

U441(X1, X2, active(X3)) → U441(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(234) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(X1, X2, active(X3)) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  U441(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U44^11

The following usable rules [FROCOS05] were oriented: none

(235) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(236) PisEmptyProof (EQUIVALENT transformation)

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

(237) TRUE

(238) Obligation:

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

U431(X1, mark(X2), X3) → U431(X1, X2, X3)
U431(mark(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, X2, mark(X3)) → U431(X1, X2, X3)
U431(active(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, active(X2), X3) → U431(X1, X2, X3)
U431(X1, X2, active(X3)) → U431(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(239) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(mark(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, X2, mark(X3)) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(240) Obligation:

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

U431(X1, mark(X2), X3) → U431(X1, X2, X3)
U431(active(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, active(X2), X3) → U431(X1, X2, X3)
U431(X1, X2, active(X3)) → U431(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(241) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(X1, mark(X2), X3) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(242) Obligation:

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

U431(active(X1), X2, X3) → U431(X1, X2, X3)
U431(X1, active(X2), X3) → U431(X1, X2, X3)
U431(X1, X2, active(X3)) → U431(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(243) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(active(X1), X2, X3) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U43^11

The following usable rules [FROCOS05] were oriented: none

(244) Obligation:

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

U431(X1, active(X2), X3) → U431(X1, X2, X3)
U431(X1, X2, active(X3)) → U431(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(245) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(X1, active(X2), X3) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U43^11

The following usable rules [FROCOS05] were oriented: none

(246) Obligation:

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

U431(X1, X2, active(X3)) → U431(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(247) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(X1, X2, active(X3)) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U43^11

The following usable rules [FROCOS05] were oriented: none

(248) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(249) PisEmptyProof (EQUIVALENT transformation)

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

(250) TRUE

(251) Obligation:

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

U421(X1, mark(X2), X3) → U421(X1, X2, X3)
U421(mark(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, X2, mark(X3)) → U421(X1, X2, X3)
U421(active(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, active(X2), X3) → U421(X1, X2, X3)
U421(X1, X2, active(X3)) → U421(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(252) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(mark(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, X2, mark(X3)) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(253) Obligation:

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

U421(X1, mark(X2), X3) → U421(X1, X2, X3)
U421(active(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, active(X2), X3) → U421(X1, X2, X3)
U421(X1, X2, active(X3)) → U421(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(254) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(X1, mark(X2), X3) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(255) Obligation:

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

U421(active(X1), X2, X3) → U421(X1, X2, X3)
U421(X1, active(X2), X3) → U421(X1, X2, X3)
U421(X1, X2, active(X3)) → U421(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(256) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(active(X1), X2, X3) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U42^11

The following usable rules [FROCOS05] were oriented: none

(257) Obligation:

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

U421(X1, active(X2), X3) → U421(X1, X2, X3)
U421(X1, X2, active(X3)) → U421(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(258) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(X1, active(X2), X3) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U42^11

The following usable rules [FROCOS05] were oriented: none

(259) Obligation:

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

U421(X1, X2, active(X3)) → U421(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(260) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(X1, X2, active(X3)) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U42^11

The following usable rules [FROCOS05] were oriented: none

(261) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(262) PisEmptyProof (EQUIVALENT transformation)

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

(263) TRUE

(264) Obligation:

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

U411(X1, mark(X2), X3) → U411(X1, X2, X3)
U411(mark(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, X2, mark(X3)) → U411(X1, X2, X3)
U411(active(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, active(X2), X3) → U411(X1, X2, X3)
U411(X1, X2, active(X3)) → U411(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(265) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(mark(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, X2, mark(X3)) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  U411(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(266) Obligation:

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

U411(X1, mark(X2), X3) → U411(X1, X2, X3)
U411(active(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, active(X2), X3) → U411(X1, X2, X3)
U411(X1, X2, active(X3)) → U411(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(267) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(X1, mark(X2), X3) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  U411(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(268) Obligation:

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

U411(active(X1), X2, X3) → U411(X1, X2, X3)
U411(X1, active(X2), X3) → U411(X1, X2, X3)
U411(X1, X2, active(X3)) → U411(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(269) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(active(X1), X2, X3) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  U411(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U41^11

The following usable rules [FROCOS05] were oriented: none

(270) Obligation:

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

U411(X1, active(X2), X3) → U411(X1, X2, X3)
U411(X1, X2, active(X3)) → U411(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(271) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(X1, active(X2), X3) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  U411(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U41^11

The following usable rules [FROCOS05] were oriented: none

(272) Obligation:

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

U411(X1, X2, active(X3)) → U411(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(273) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(X1, X2, active(X3)) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  U411(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U41^11

The following usable rules [FROCOS05] were oriented: none

(274) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(275) PisEmptyProof (EQUIVALENT transformation)

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

(276) TRUE

(277) Obligation:

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

ISQID(active(X)) → ISQID(X)
ISQID(mark(X)) → ISQID(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(278) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISQID(active(X)) → ISQID(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ISQID(x1)  =  ISQID(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > ISQID1

The following usable rules [FROCOS05] were oriented: none

(279) Obligation:

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

ISQID(mark(X)) → ISQID(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(280) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISQID(mark(X)) → ISQID(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > ISQID1

The following usable rules [FROCOS05] were oriented: none

(281) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(282) PisEmptyProof (EQUIVALENT transformation)

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

(283) TRUE

(284) Obligation:

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

U331(active(X)) → U331(X)
U331(mark(X)) → U331(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(285) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U331(active(X)) → U331(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U331(x1)  =  U331(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U33^11

The following usable rules [FROCOS05] were oriented: none

(286) Obligation:

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

U331(mark(X)) → U331(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(287) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U331(mark(X)) → U331(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U33^11

The following usable rules [FROCOS05] were oriented: none

(288) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(289) PisEmptyProof (EQUIVALENT transformation)

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

(290) TRUE

(291) Obligation:

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

U321(X1, mark(X2)) → U321(X1, X2)
U321(mark(X1), X2) → U321(X1, X2)
U321(active(X1), X2) → U321(X1, X2)
U321(X1, active(X2)) → U321(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(292) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U321(X1, mark(X2)) → U321(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U321(x1, x2)  =  U321(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U32^11

The following usable rules [FROCOS05] were oriented: none

(293) Obligation:

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

U321(mark(X1), X2) → U321(X1, X2)
U321(active(X1), X2) → U321(X1, X2)
U321(X1, active(X2)) → U321(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(294) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U321(mark(X1), X2) → U321(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U321(x1, x2)  =  U321(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U32^12

The following usable rules [FROCOS05] were oriented: none

(295) Obligation:

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

U321(active(X1), X2) → U321(X1, X2)
U321(X1, active(X2)) → U321(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(296) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U321(active(X1), X2) → U321(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U321(x1, x2)  =  U321(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U32^11

The following usable rules [FROCOS05] were oriented: none

(297) Obligation:

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

U321(X1, active(X2)) → U321(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(298) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U321(X1, active(X2)) → U321(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U321(x1, x2)  =  U321(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U32^11

The following usable rules [FROCOS05] were oriented: none

(299) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(300) PisEmptyProof (EQUIVALENT transformation)

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

(301) TRUE

(302) Obligation:

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

U311(X1, mark(X2)) → U311(X1, X2)
U311(mark(X1), X2) → U311(X1, X2)
U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(303) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U311(X1, mark(X2)) → U311(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U311(x1, x2)  =  U311(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U31^11

The following usable rules [FROCOS05] were oriented: none

(304) Obligation:

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

U311(mark(X1), X2) → U311(X1, X2)
U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(305) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U311(mark(X1), X2) → U311(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U311(x1, x2)  =  U311(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U31^12

The following usable rules [FROCOS05] were oriented: none

(306) Obligation:

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

U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(307) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U311(active(X1), X2) → U311(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U311(x1, x2)  =  U311(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U31^11

The following usable rules [FROCOS05] were oriented: none

(308) Obligation:

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

U311(X1, active(X2)) → U311(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(309) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U311(X1, active(X2)) → U311(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U311(x1, x2)  =  U311(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U31^11

The following usable rules [FROCOS05] were oriented: none

(310) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(311) PisEmptyProof (EQUIVALENT transformation)

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

(312) TRUE

(313) Obligation:

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

U261(active(X)) → U261(X)
U261(mark(X)) → U261(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(314) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U261(active(X)) → U261(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U261(x1)  =  U261(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U26^11

The following usable rules [FROCOS05] were oriented: none

(315) Obligation:

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

U261(mark(X)) → U261(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(316) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U261(mark(X)) → U261(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U26^11

The following usable rules [FROCOS05] were oriented: none

(317) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(318) PisEmptyProof (EQUIVALENT transformation)

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

(319) TRUE

(320) Obligation:

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

ISLIST(active(X)) → ISLIST(X)
ISLIST(mark(X)) → ISLIST(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(321) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISLIST(active(X)) → ISLIST(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ISLIST(x1)  =  ISLIST(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > ISLIST1

The following usable rules [FROCOS05] were oriented: none

(322) Obligation:

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

ISLIST(mark(X)) → ISLIST(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(323) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISLIST(mark(X)) → ISLIST(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > ISLIST1

The following usable rules [FROCOS05] were oriented: none

(324) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(325) PisEmptyProof (EQUIVALENT transformation)

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

(326) TRUE

(327) Obligation:

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

U251(X1, mark(X2)) → U251(X1, X2)
U251(mark(X1), X2) → U251(X1, X2)
U251(active(X1), X2) → U251(X1, X2)
U251(X1, active(X2)) → U251(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(328) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U251(X1, mark(X2)) → U251(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U251(x1, x2)  =  U251(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U25^11

The following usable rules [FROCOS05] were oriented: none

(329) Obligation:

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

U251(mark(X1), X2) → U251(X1, X2)
U251(active(X1), X2) → U251(X1, X2)
U251(X1, active(X2)) → U251(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(330) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U251(mark(X1), X2) → U251(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U251(x1, x2)  =  U251(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U25^12

The following usable rules [FROCOS05] were oriented: none

(331) Obligation:

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

U251(active(X1), X2) → U251(X1, X2)
U251(X1, active(X2)) → U251(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(332) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U251(active(X1), X2) → U251(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U251(x1, x2)  =  U251(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U25^11

The following usable rules [FROCOS05] were oriented: none

(333) Obligation:

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

U251(X1, active(X2)) → U251(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(334) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U251(X1, active(X2)) → U251(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U251(x1, x2)  =  U251(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U25^11

The following usable rules [FROCOS05] were oriented: none

(335) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(336) PisEmptyProof (EQUIVALENT transformation)

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

(337) TRUE

(338) Obligation:

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

U241(X1, mark(X2), X3) → U241(X1, X2, X3)
U241(mark(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, X2, mark(X3)) → U241(X1, X2, X3)
U241(active(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, active(X2), X3) → U241(X1, X2, X3)
U241(X1, X2, active(X3)) → U241(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(339) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(mark(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, X2, mark(X3)) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(340) Obligation:

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

U241(X1, mark(X2), X3) → U241(X1, X2, X3)
U241(active(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, active(X2), X3) → U241(X1, X2, X3)
U241(X1, X2, active(X3)) → U241(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(341) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(X1, mark(X2), X3) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(342) Obligation:

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

U241(active(X1), X2, X3) → U241(X1, X2, X3)
U241(X1, active(X2), X3) → U241(X1, X2, X3)
U241(X1, X2, active(X3)) → U241(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(343) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(active(X1), X2, X3) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U24^11

The following usable rules [FROCOS05] were oriented: none

(344) Obligation:

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

U241(X1, active(X2), X3) → U241(X1, X2, X3)
U241(X1, X2, active(X3)) → U241(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(345) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(X1, active(X2), X3) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U24^11

The following usable rules [FROCOS05] were oriented: none

(346) Obligation:

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

U241(X1, X2, active(X3)) → U241(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(347) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(X1, X2, active(X3)) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U24^11

The following usable rules [FROCOS05] were oriented: none

(348) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(349) PisEmptyProof (EQUIVALENT transformation)

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

(350) TRUE

(351) Obligation:

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

U231(X1, mark(X2), X3) → U231(X1, X2, X3)
U231(mark(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, X2, mark(X3)) → U231(X1, X2, X3)
U231(active(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, active(X2), X3) → U231(X1, X2, X3)
U231(X1, X2, active(X3)) → U231(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(352) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(mark(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, X2, mark(X3)) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(353) Obligation:

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

U231(X1, mark(X2), X3) → U231(X1, X2, X3)
U231(active(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, active(X2), X3) → U231(X1, X2, X3)
U231(X1, X2, active(X3)) → U231(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(354) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(X1, mark(X2), X3) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(355) Obligation:

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

U231(active(X1), X2, X3) → U231(X1, X2, X3)
U231(X1, active(X2), X3) → U231(X1, X2, X3)
U231(X1, X2, active(X3)) → U231(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(356) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(active(X1), X2, X3) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U23^11

The following usable rules [FROCOS05] were oriented: none

(357) Obligation:

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

U231(X1, active(X2), X3) → U231(X1, X2, X3)
U231(X1, X2, active(X3)) → U231(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(358) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(X1, active(X2), X3) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U23^11

The following usable rules [FROCOS05] were oriented: none

(359) Obligation:

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

U231(X1, X2, active(X3)) → U231(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(360) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(X1, X2, active(X3)) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U23^11

The following usable rules [FROCOS05] were oriented: none

(361) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(362) PisEmptyProof (EQUIVALENT transformation)

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

(363) TRUE

(364) Obligation:

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

U221(X1, mark(X2), X3) → U221(X1, X2, X3)
U221(mark(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, X2, mark(X3)) → U221(X1, X2, X3)
U221(active(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, active(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, active(X3)) → U221(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(365) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(mark(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, X2, mark(X3)) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(366) Obligation:

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

U221(X1, mark(X2), X3) → U221(X1, X2, X3)
U221(active(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, active(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, active(X3)) → U221(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(367) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(X1, mark(X2), X3) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(368) Obligation:

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

U221(active(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, active(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, active(X3)) → U221(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(369) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(active(X1), X2, X3) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U22^11

The following usable rules [FROCOS05] were oriented: none

(370) Obligation:

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

U221(X1, active(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, active(X3)) → U221(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(371) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(X1, active(X2), X3) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U22^11

The following usable rules [FROCOS05] were oriented: none

(372) Obligation:

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

U221(X1, X2, active(X3)) → U221(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(373) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(X1, X2, active(X3)) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U22^11

The following usable rules [FROCOS05] were oriented: none

(374) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(375) PisEmptyProof (EQUIVALENT transformation)

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

(376) TRUE

(377) Obligation:

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

U211(X1, mark(X2), X3) → U211(X1, X2, X3)
U211(mark(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, X2, mark(X3)) → U211(X1, X2, X3)
U211(active(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, active(X2), X3) → U211(X1, X2, X3)
U211(X1, X2, active(X3)) → U211(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(378) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(mark(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, X2, mark(X3)) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(379) Obligation:

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

U211(X1, mark(X2), X3) → U211(X1, X2, X3)
U211(active(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, active(X2), X3) → U211(X1, X2, X3)
U211(X1, X2, active(X3)) → U211(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(380) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(X1, mark(X2), X3) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
trivial

The following usable rules [FROCOS05] were oriented: none

(381) Obligation:

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

U211(active(X1), X2, X3) → U211(X1, X2, X3)
U211(X1, active(X2), X3) → U211(X1, X2, X3)
U211(X1, X2, active(X3)) → U211(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(382) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(active(X1), X2, X3) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U21^11

The following usable rules [FROCOS05] were oriented: none

(383) Obligation:

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

U211(X1, active(X2), X3) → U211(X1, X2, X3)
U211(X1, X2, active(X3)) → U211(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(384) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(X1, active(X2), X3) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U21^11

The following usable rules [FROCOS05] were oriented: none

(385) Obligation:

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

U211(X1, X2, active(X3)) → U211(X1, X2, X3)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(386) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(X1, X2, active(X3)) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x3)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U21^11

The following usable rules [FROCOS05] were oriented: none

(387) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(388) PisEmptyProof (EQUIVALENT transformation)

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

(389) TRUE

(390) Obligation:

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

ISNELIST(active(X)) → ISNELIST(X)
ISNELIST(mark(X)) → ISNELIST(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(391) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISNELIST(active(X)) → ISNELIST(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ISNELIST(x1)  =  ISNELIST(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > ISNELIST1

The following usable rules [FROCOS05] were oriented: none

(392) Obligation:

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

ISNELIST(mark(X)) → ISNELIST(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(393) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISNELIST(mark(X)) → ISNELIST(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > ISNELIST1

The following usable rules [FROCOS05] were oriented: none

(394) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(395) PisEmptyProof (EQUIVALENT transformation)

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

(396) TRUE

(397) Obligation:

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

U131(active(X)) → U131(X)
U131(mark(X)) → U131(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(398) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U131(active(X)) → U131(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U131(x1)  =  U131(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > U13^11

The following usable rules [FROCOS05] were oriented: none

(399) Obligation:

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

U131(mark(X)) → U131(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(400) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U131(mark(X)) → U131(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > U13^11

The following usable rules [FROCOS05] were oriented: none

(401) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(402) PisEmptyProof (EQUIVALENT transformation)

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

(403) TRUE

(404) Obligation:

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

ISPALLISTKIND(active(X)) → ISPALLISTKIND(X)
ISPALLISTKIND(mark(X)) → ISPALLISTKIND(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(405) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISPALLISTKIND(active(X)) → ISPALLISTKIND(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ISPALLISTKIND(x1)  =  ISPALLISTKIND(x1)
active(x1)  =  active(x1)
mark(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
active1 > ISPALLISTKIND1

The following usable rules [FROCOS05] were oriented: none

(406) Obligation:

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

ISPALLISTKIND(mark(X)) → ISPALLISTKIND(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(407) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ISPALLISTKIND(mark(X)) → ISPALLISTKIND(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Recursive Path Order [RPO].
Precedence:
mark1 > ISPALLISTKIND1

The following usable rules [FROCOS05] were oriented: none

(408) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(409) PisEmptyProof (EQUIVALENT transformation)

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

(410) TRUE

(411) Obligation:

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

U121(X1, mark(X2)) → U121(X1, X2)
U121(mark(X1), X2) → U121(X1, X2)
U121(active(X1), X2) → U121(X1, X2)
U121(X1, active(X2)) → U121(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(412) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U121(X1, mark(X2)) → U121(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U121(x1, x2)  =  U121(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U12^11

The following usable rules [FROCOS05] were oriented: none

(413) Obligation:

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

U121(mark(X1), X2) → U121(X1, X2)
U121(active(X1), X2) → U121(X1, X2)
U121(X1, active(X2)) → U121(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(414) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U121(mark(X1), X2) → U121(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U121(x1, x2)  =  U121(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U12^12

The following usable rules [FROCOS05] were oriented: none

(415) Obligation:

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

U121(active(X1), X2) → U121(X1, X2)
U121(X1, active(X2)) → U121(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(416) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U121(active(X1), X2) → U121(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U121(x1, x2)  =  U121(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U12^11

The following usable rules [FROCOS05] were oriented: none

(417) Obligation:

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

U121(X1, active(X2)) → U121(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(418) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U121(X1, active(X2)) → U121(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U121(x1, x2)  =  U121(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U12^11

The following usable rules [FROCOS05] were oriented: none

(419) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(420) PisEmptyProof (EQUIVALENT transformation)

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

(421) TRUE

(422) Obligation:

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

U111(X1, mark(X2)) → U111(X1, X2)
U111(mark(X1), X2) → U111(X1, X2)
U111(active(X1), X2) → U111(X1, X2)
U111(X1, active(X2)) → U111(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(423) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U111(X1, mark(X2)) → U111(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U111(x1, x2)  =  U111(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U11^11

The following usable rules [FROCOS05] were oriented: none

(424) Obligation:

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

U111(mark(X1), X2) → U111(X1, X2)
U111(active(X1), X2) → U111(X1, X2)
U111(X1, active(X2)) → U111(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(425) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U111(mark(X1), X2) → U111(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U111(x1, x2)  =  U111(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > U11^12

The following usable rules [FROCOS05] were oriented: none

(426) Obligation:

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

U111(active(X1), X2) → U111(X1, X2)
U111(X1, active(X2)) → U111(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(427) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U111(active(X1), X2) → U111(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U111(x1, x2)  =  U111(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U11^11

The following usable rules [FROCOS05] were oriented: none

(428) Obligation:

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

U111(X1, active(X2)) → U111(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(429) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U111(X1, active(X2)) → U111(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U111(x1, x2)  =  U111(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > U11^11

The following usable rules [FROCOS05] were oriented: none

(430) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(431) PisEmptyProof (EQUIVALENT transformation)

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

(432) TRUE

(433) Obligation:

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

__1(X1, mark(X2)) → __1(X1, X2)
__1(mark(X1), X2) → __1(X1, X2)
__1(active(X1), X2) → __1(X1, X2)
__1(X1, active(X2)) → __1(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(434) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(X1, mark(X2)) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  __1(x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > _^11

The following usable rules [FROCOS05] were oriented: none

(435) Obligation:

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

__1(mark(X1), X2) → __1(X1, X2)
__1(active(X1), X2) → __1(X1, X2)
__1(X1, active(X2)) → __1(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(436) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(mark(X1), X2) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  __1(x1, x2)
mark(x1)  =  mark(x1)
active(x1)  =  x1

Recursive Path Order [RPO].
Precedence:
mark1 > _^12

The following usable rules [FROCOS05] were oriented: none

(437) Obligation:

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

__1(active(X1), X2) → __1(X1, X2)
__1(X1, active(X2)) → __1(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(438) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(active(X1), X2) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  __1(x1)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > _^11

The following usable rules [FROCOS05] were oriented: none

(439) Obligation:

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

__1(X1, active(X2)) → __1(X1, X2)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(440) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(X1, active(X2)) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  __1(x2)
active(x1)  =  active(x1)

Recursive Path Order [RPO].
Precedence:
active1 > _^11

The following usable rules [FROCOS05] were oriented: none

(441) Obligation:

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

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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

(442) PisEmptyProof (EQUIVALENT transformation)

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

(443) TRUE

(444) Obligation:

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

MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U11(X1, X2)) → ACTIVE(U11(mark(X1), X2))
ACTIVE(__(X, nil)) → MARK(X)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U12(X1, X2)) → ACTIVE(U12(mark(X1), X2))
ACTIVE(__(nil, X)) → MARK(X)
MARK(U12(X1, X2)) → MARK(X1)
MARK(isPalListKind(X)) → ACTIVE(isPalListKind(X))
ACTIVE(U11(tt, V)) → MARK(U12(isPalListKind(V), V))
MARK(U13(X)) → ACTIVE(U13(mark(X)))
ACTIVE(U12(tt, V)) → MARK(U13(isNeList(V)))
MARK(U13(X)) → MARK(X)
MARK(isNeList(X)) → ACTIVE(isNeList(X))
ACTIVE(U21(tt, V1, V2)) → MARK(U22(isPalListKind(V1), V1, V2))
MARK(U21(X1, X2, X3)) → ACTIVE(U21(mark(X1), X2, X3))
ACTIVE(U22(tt, V1, V2)) → MARK(U23(isPalListKind(V2), V1, V2))
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → ACTIVE(U22(mark(X1), X2, X3))
ACTIVE(U23(tt, V1, V2)) → MARK(U24(isPalListKind(V2), V1, V2))
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → ACTIVE(U23(mark(X1), X2, X3))
ACTIVE(U24(tt, V1, V2)) → MARK(U25(isList(V1), V2))
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → ACTIVE(U24(mark(X1), X2, X3))
ACTIVE(U25(tt, V2)) → MARK(U26(isList(V2)))
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → ACTIVE(U25(mark(X1), X2))
ACTIVE(U31(tt, V)) → MARK(U32(isPalListKind(V), V))
MARK(U25(X1, X2)) → MARK(X1)
MARK(isList(X)) → ACTIVE(isList(X))
ACTIVE(U32(tt, V)) → MARK(U33(isQid(V)))
MARK(U26(X)) → ACTIVE(U26(mark(X)))
ACTIVE(U41(tt, V1, V2)) → MARK(U42(isPalListKind(V1), V1, V2))
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U42(tt, V1, V2)) → MARK(U43(isPalListKind(V2), V1, V2))
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → ACTIVE(U32(mark(X1), X2))
ACTIVE(U43(tt, V1, V2)) → MARK(U44(isPalListKind(V2), V1, V2))
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → ACTIVE(U33(mark(X)))
ACTIVE(U44(tt, V1, V2)) → MARK(U45(isList(V1), V2))
MARK(U33(X)) → MARK(X)
MARK(isQid(X)) → ACTIVE(isQid(X))
ACTIVE(U45(tt, V2)) → MARK(U46(isNeList(V2)))
MARK(U41(X1, X2, X3)) → ACTIVE(U41(mark(X1), X2, X3))
ACTIVE(U51(tt, V1, V2)) → MARK(U52(isPalListKind(V1), V1, V2))
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → ACTIVE(U42(mark(X1), X2, X3))
ACTIVE(U52(tt, V1, V2)) → MARK(U53(isPalListKind(V2), V1, V2))
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → ACTIVE(U43(mark(X1), X2, X3))
ACTIVE(U53(tt, V1, V2)) → MARK(U54(isPalListKind(V2), V1, V2))
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → ACTIVE(U44(mark(X1), X2, X3))
ACTIVE(U54(tt, V1, V2)) → MARK(U55(isNeList(V1), V2))
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → ACTIVE(U45(mark(X1), X2))
ACTIVE(U55(tt, V2)) → MARK(U56(isList(V2)))
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → ACTIVE(U46(mark(X)))
ACTIVE(U61(tt, V)) → MARK(U62(isPalListKind(V), V))
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → ACTIVE(U51(mark(X1), X2, X3))
ACTIVE(U62(tt, V)) → MARK(U63(isQid(V)))
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → ACTIVE(U52(mark(X1), X2, X3))
ACTIVE(U71(tt, I, P)) → MARK(U72(isPalListKind(I), P))
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → ACTIVE(U53(mark(X1), X2, X3))
ACTIVE(U72(tt, P)) → MARK(U73(isPal(P), P))
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → ACTIVE(U54(mark(X1), X2, X3))
ACTIVE(U73(tt, P)) → MARK(U74(isPalListKind(P)))
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → ACTIVE(U55(mark(X1), X2))
ACTIVE(U81(tt, V)) → MARK(U82(isPalListKind(V), V))
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → ACTIVE(U56(mark(X)))
ACTIVE(U82(tt, V)) → MARK(U83(isNePal(V)))
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
ACTIVE(U91(tt, V2)) → MARK(U92(isPalListKind(V2)))
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → ACTIVE(U62(mark(X1), X2))
ACTIVE(isList(V)) → MARK(U11(isPalListKind(V), V))
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → ACTIVE(U63(mark(X)))
ACTIVE(isList(__(V1, V2))) → MARK(U21(isPalListKind(V1), V1, V2))
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → ACTIVE(U71(mark(X1), X2, X3))
ACTIVE(isNeList(V)) → MARK(U31(isPalListKind(V), V))
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → ACTIVE(U72(mark(X1), X2))
ACTIVE(isNeList(__(V1, V2))) → MARK(U41(isPalListKind(V1), V1, V2))
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → ACTIVE(U73(mark(X1), X2))
ACTIVE(isNeList(__(V1, V2))) → MARK(U51(isPalListKind(V1), V1, V2))
MARK(U73(X1, X2)) → MARK(X1)
MARK(isPal(X)) → ACTIVE(isPal(X))
ACTIVE(isNePal(V)) → MARK(U61(isPalListKind(V), V))
MARK(U74(X)) → ACTIVE(U74(mark(X)))
ACTIVE(isNePal(__(I, __(P, I)))) → MARK(U71(isQid(I), I, P))
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → ACTIVE(U81(mark(X1), X2))
ACTIVE(isPal(V)) → MARK(U81(isPalListKind(V), V))
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → ACTIVE(U82(mark(X1), X2))
ACTIVE(isPalListKind(__(V1, V2))) → MARK(U91(isPalListKind(V1), V2))
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → ACTIVE(U83(mark(X)))
MARK(U83(X)) → MARK(X)
MARK(isNePal(X)) → ACTIVE(isNePal(X))
MARK(U91(X1, X2)) → ACTIVE(U91(mark(X1), X2))
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → ACTIVE(U92(mark(X)))
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(U11(X1, X2)) → active(U11(mark(X1), X2))
mark(tt) → active(tt)
mark(U12(X1, X2)) → active(U12(mark(X1), X2))
mark(isPalListKind(X)) → active(isPalListKind(X))
mark(U13(X)) → active(U13(mark(X)))
mark(isNeList(X)) → active(isNeList(X))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))
mark(U22(X1, X2, X3)) → active(U22(mark(X1), X2, X3))
mark(U23(X1, X2, X3)) → active(U23(mark(X1), X2, X3))
mark(U24(X1, X2, X3)) → active(U24(mark(X1), X2, X3))
mark(U25(X1, X2)) → active(U25(mark(X1), X2))
mark(isList(X)) → active(isList(X))
mark(U26(X)) → active(U26(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))
mark(U33(X)) → active(U33(mark(X)))
mark(isQid(X)) → active(isQid(X))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2, X3)) → active(U42(mark(X1), X2, X3))
mark(U43(X1, X2, X3)) → active(U43(mark(X1), X2, X3))
mark(U44(X1, X2, X3)) → active(U44(mark(X1), X2, X3))
mark(U45(X1, X2)) → active(U45(mark(X1), X2))
mark(U46(X)) → active(U46(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2, X3)) → active(U52(mark(X1), X2, X3))
mark(U53(X1, X2, X3)) → active(U53(mark(X1), X2, X3))
mark(U54(X1, X2, X3)) → active(U54(mark(X1), X2, X3))
mark(U55(X1, X2)) → active(U55(mark(X1), X2))
mark(U56(X)) → active(U56(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X1, X2)) → active(U62(mark(X1), X2))
mark(U63(X)) → active(U63(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(U73(X1, X2)) → active(U73(mark(X1), X2))
mark(isPal(X)) → active(isPal(X))
mark(U74(X)) → active(U74(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X1, X2)) → active(U82(mark(X1), X2))
mark(U83(X)) → active(U83(mark(X)))
mark(isNePal(X)) → active(isNePal(X))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(a) → active(a)
mark(e) → active(e)
mark(i) → active(i)
mark(o) → active(o)
mark(u) → active(u)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(X1, mark(X2)) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(mark(X)) → isPalListKind(X)
isPalListKind(active(X)) → isPalListKind(X)
U13(mark(X)) → U13(X)
U13(active(X)) → U13(X)
isNeList(mark(X)) → isNeList(X)
isNeList(active(X)) → isNeList(X)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)
U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, mark(X3)) → U22(X1, X2, X3)
U22(active(X1), X2, X3) → U22(X1, X2, X3)
U22(X1, active(X2), X3) → U22(X1, X2, X3)
U22(X1, X2, active(X3)) → U22(X1, X2, X3)
U23(mark(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, mark(X3)) → U23(X1, X2, X3)
U23(active(X1), X2, X3) → U23(X1, X2, X3)
U23(X1, active(X2), X3) → U23(X1, X2, X3)
U23(X1, X2, active(X3)) → U23(X1, X2, X3)
U24(mark(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, mark(X3)) → U24(X1, X2, X3)
U24(active(X1), X2, X3) → U24(X1, X2, X3)
U24(X1, active(X2), X3) → U24(X1, X2, X3)
U24(X1, X2, active(X3)) → U24(X1, X2, X3)
U25(mark(X1), X2) → U25(X1, X2)
U25(X1, mark(X2)) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(mark(X)) → isList(X)
isList(active(X)) → isList(X)
U26(mark(X)) → U26(X)
U26(active(X)) → U26(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(mark(X)) → U33(X)
U33(active(X)) → U33(X)
isQid(mark(X)) → isQid(X)
isQid(active(X)) → isQid(X)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, mark(X3)) → U42(X1, X2, X3)
U42(active(X1), X2, X3) → U42(X1, X2, X3)
U42(X1, active(X2), X3) → U42(X1, X2, X3)
U42(X1, X2, active(X3)) → U42(X1, X2, X3)
U43(mark(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, mark(X3)) → U43(X1, X2, X3)
U43(active(X1), X2, X3) → U43(X1, X2, X3)
U43(X1, active(X2), X3) → U43(X1, X2, X3)
U43(X1, X2, active(X3)) → U43(X1, X2, X3)
U44(mark(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, mark(X3)) → U44(X1, X2, X3)
U44(active(X1), X2, X3) → U44(X1, X2, X3)
U44(X1, active(X2), X3) → U44(X1, X2, X3)
U44(X1, X2, active(X3)) → U44(X1, X2, X3)
U45(mark(X1), X2) → U45(X1, X2)
U45(X1, mark(X2)) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U46(mark(X)) → U46(X)
U46(active(X)) → U46(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, mark(X3)) → U52(X1, X2, X3)
U52(active(X1), X2, X3) → U52(X1, X2, X3)
U52(X1, active(X2), X3) → U52(X1, X2, X3)
U52(X1, X2, active(X3)) → U52(X1, X2, X3)
U53(mark(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, mark(X3)) → U53(X1, X2, X3)
U53(active(X1), X2, X3) → U53(X1, X2, X3)
U53(X1, active(X2), X3) → U53(X1, X2, X3)
U53(X1, X2, active(X3)) → U53(X1, X2, X3)
U54(mark(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, mark(X3)) → U54(X1, X2, X3)
U54(active(X1), X2, X3) → U54(X1, X2, X3)
U54(X1, active(X2), X3) → U54(X1, X2, X3)
U54(X1, X2, active(X3)) → U54(X1, X2, X3)
U55(mark(X1), X2) → U55(X1, X2)
U55(X1, mark(X2)) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U56(mark(X)) → U56(X)
U56(active(X)) → U56(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U63(mark(X)) → U63(X)
U63(active(X)) → U63(X)
U71(mark(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
isPal(mark(X)) → isPal(X)
isPal(active(X)) → isPal(X)
U74(mark(X)) → U74(X)
U74(active(X)) → U74(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U83(mark(X)) → U83(X)
U83(active(X)) → U83(X)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)

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