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

(0) Obligation:

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

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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

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: Combined order from the following AFS and order.
U92¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

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, 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(14) 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)

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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(16) Obligation:

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

U91¹(X1, mark(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(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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(18) 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.

(19) PisEmptyProof (EQUIVALENT transformation)

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

(20) TRUE

(21) 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.

(22) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(23) 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.

(24) 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: Combined order from the following AFS and order.
ISNEPAL(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(25) 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.

(26) PisEmptyProof (EQUIVALENT transformation)

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

(27) TRUE

(28) 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.

(29) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(30) Obligation:

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

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(mark(X)) → U83¹(X)

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

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(32) 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.

(33) PisEmptyProof (EQUIVALENT transformation)

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

(34) TRUE

(35) 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.

(36) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(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)

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(mark(X1), X2) → U82¹(X1, X2)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(39) Obligation:

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

U82¹(X1, mark(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(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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(41) 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.

(42) PisEmptyProof (EQUIVALENT transformation)

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

(43) TRUE

(44) 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.

(45) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(46) Obligation:

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

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

(47) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(48) Obligation:

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

U81¹(X1, mark(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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(50) 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.

(51) PisEmptyProof (EQUIVALENT transformation)

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

(52) TRUE

(53) 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.

(54) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(55) 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.

(56) 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: Combined order from the following AFS and order.
U74¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(57) 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.

(58) PisEmptyProof (EQUIVALENT transformation)

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

(59) TRUE

(60) 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.

(61) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(62) Obligation:

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

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.

(63) 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: Combined order from the following AFS and order.
ISPAL(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(64) 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.

(65) PisEmptyProof (EQUIVALENT transformation)

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

(66) TRUE

(67) 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.

(68) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(69) 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)

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.

(70) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(71) Obligation:

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

U73¹(X1, mark(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.

(72) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(73) 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.

(74) PisEmptyProof (EQUIVALENT transformation)

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

(75) TRUE

(76) 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.

(77) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(78) Obligation:

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

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

(79) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(80) Obligation:

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

U72¹(X1, mark(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.

(81) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(82) 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.

(83) PisEmptyProof (EQUIVALENT transformation)

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

(84) TRUE

(85) 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.

(86) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(87) 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, 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.

(88) 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)
U71¹(active(X1), X2, X3) → U71¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U71^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(89) Obligation:

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

U71¹(X1, mark(X2), 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.

(90) 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)

Lexicographic Path Order [LPO].
Precedence:

[U71^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(91) 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.

(92) PisEmptyProof (EQUIVALENT transformation)

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

(93) TRUE

(94) 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.

(95) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(96) 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.

(97) 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: Combined order from the following AFS and order.
U63¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(98) 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.

(99) PisEmptyProof (EQUIVALENT transformation)

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

(100) TRUE

(101) 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.

(102) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(103) 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)

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.

U62¹(mark(X1), X2) → U62¹(X1, X2)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(105) Obligation:

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

U62¹(X1, mark(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.

(106) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(107) 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.

(108) PisEmptyProof (EQUIVALENT transformation)

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

(109) TRUE

(110) 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.

(111) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(112) 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)

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) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(114) Obligation:

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

U61¹(X1, mark(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.

(115) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(116) 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.

(117) PisEmptyProof (EQUIVALENT transformation)

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

(118) TRUE

(119) 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.

(120) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(121) 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.

(122) 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: Combined order from the following AFS and order.
U56¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

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:

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.

(127) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(128) 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)

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.

U55¹(mark(X1), X2) → U55¹(X1, X2)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(130) Obligation:

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

U55¹(X1, mark(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.

(131) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(132) 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.

(133) PisEmptyProof (EQUIVALENT transformation)

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

(134) TRUE

(135) 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.

(136) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(137) 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, 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.

(138) 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)
U54¹(active(X1), X2, X3) → U54¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U54^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(139) Obligation:

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

U54¹(X1, mark(X2), 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.

(140) 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)

Lexicographic Path Order [LPO].
Precedence:

[U54^1₂, mark₁]

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:

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.

(145) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(146) 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, 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.

(147) 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)
U53¹(active(X1), X2, X3) → U53¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U53^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(148) Obligation:

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

U53¹(X1, mark(X2), 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.

(149) 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)

Lexicographic Path Order [LPO].
Precedence:

[U53^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(150) 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.

(151) PisEmptyProof (EQUIVALENT transformation)

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

(152) TRUE

(153) 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.

(154) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(155) 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, 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.

(156) 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)
U52¹(active(X1), X2, X3) → U52¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U52^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(157) Obligation:

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

U52¹(X1, mark(X2), 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.

(158) 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)

Lexicographic Path Order [LPO].
Precedence:

[U52^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(159) 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.

(160) PisEmptyProof (EQUIVALENT transformation)

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

(161) TRUE

(162) 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.

(163) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(164) 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, 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.

(165) 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)
U51¹(active(X1), X2, X3) → U51¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U51^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(166) Obligation:

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

U51¹(X1, mark(X2), 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.

(167) 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)

Lexicographic Path Order [LPO].
Precedence:

[U51^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(168) 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.

(169) PisEmptyProof (EQUIVALENT transformation)

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

(170) TRUE

(171) 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.

(172) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(173) 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.

(174) 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: Combined order from the following AFS and order.
U46¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(175) 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.

(176) PisEmptyProof (EQUIVALENT transformation)

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

(177) TRUE

(178) 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.

(179) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(180) 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)

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.

(181) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(182) Obligation:

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

U45¹(X1, mark(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.

(183) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(184) 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.

(185) PisEmptyProof (EQUIVALENT transformation)

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

(186) TRUE

(187) 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.

(188) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(189) 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, 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.

(190) 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)
U44¹(active(X1), X2, X3) → U44¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U44^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(191) Obligation:

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

U44¹(X1, mark(X2), 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.

(192) 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)

Lexicographic Path Order [LPO].
Precedence:

[U44^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(193) 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.

(194) PisEmptyProof (EQUIVALENT transformation)

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

(195) TRUE

(196) 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.

(197) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(198) 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, 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.

(199) 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)
U43¹(active(X1), X2, X3) → U43¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U43^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(200) Obligation:

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

U43¹(X1, mark(X2), 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.

(201) 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)

Lexicographic Path Order [LPO].
Precedence:

[U43^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(202) 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.

(203) PisEmptyProof (EQUIVALENT transformation)

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

(204) TRUE

(205) 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.

(206) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(207) 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, 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.

(208) 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)
U42¹(active(X1), X2, X3) → U42¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U42^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(209) Obligation:

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

U42¹(X1, mark(X2), 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.

(210) 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)

Lexicographic Path Order [LPO].
Precedence:

[U42^1₂, mark₁]

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:

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.

(215) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(216) 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, 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.

(217) 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)
U41¹(active(X1), X2, X3) → U41¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U41^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(218) Obligation:

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

U41¹(X1, mark(X2), 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.

(219) 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)

Lexicographic Path Order [LPO].
Precedence:

[U41^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(220) 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.

(221) PisEmptyProof (EQUIVALENT transformation)

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

(222) TRUE

(223) 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.

(224) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(225) 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.

(226) 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: Combined order from the following AFS and order.
ISQID(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(227) 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.

(228) PisEmptyProof (EQUIVALENT transformation)

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

(229) TRUE

(230) 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.

(231) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(232) 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.

(233) 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: Combined order from the following AFS and order.
U33¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(234) 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.

(235) PisEmptyProof (EQUIVALENT transformation)

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

(236) TRUE

(237) 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.

(238) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(239) 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)

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.

(240) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(241) Obligation:

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

U32¹(X1, mark(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.

(242) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(243) 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.

(244) PisEmptyProof (EQUIVALENT transformation)

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

(245) TRUE

(246) 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.

(247) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(248) 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)

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) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(250) Obligation:

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

U31¹(X1, mark(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.

(251) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(252) 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.

(253) PisEmptyProof (EQUIVALENT transformation)

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

(254) TRUE

(255) 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.

(256) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(257) 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.

(258) 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: Combined order from the following AFS and order.
U26¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(259) 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.

(260) PisEmptyProof (EQUIVALENT transformation)

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

(261) TRUE

(262) 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.

(263) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(264) 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.

(265) 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: Combined order from the following AFS and order.
ISLIST(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(266) 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.

(267) PisEmptyProof (EQUIVALENT transformation)

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

(268) TRUE

(269) 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.

(270) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(271) 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)

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.

(272) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(273) Obligation:

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

U25¹(X1, mark(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.

(274) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(275) 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.

(276) PisEmptyProof (EQUIVALENT transformation)

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

(277) TRUE

(278) 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.

(279) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(280) 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, 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.

(281) 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)
U24¹(active(X1), X2, X3) → U24¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U24^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(282) Obligation:

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

U24¹(X1, mark(X2), 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.

(283) 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)

Lexicographic Path Order [LPO].
Precedence:

[U24^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(284) 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.

(285) PisEmptyProof (EQUIVALENT transformation)

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

(286) TRUE

(287) 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.

(288) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(289) 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, 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.

(290) 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)
U23¹(active(X1), X2, X3) → U23¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U23^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(291) Obligation:

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

U23¹(X1, mark(X2), 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.

(292) 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)

Lexicographic Path Order [LPO].
Precedence:

[U23^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(293) 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.

(294) PisEmptyProof (EQUIVALENT transformation)

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

(295) TRUE

(296) 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.

(297) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(298) 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, 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.

(299) 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)
U22¹(active(X1), X2, X3) → U22¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U22^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(300) Obligation:

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

U22¹(X1, mark(X2), 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.

(301) 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)

Lexicographic Path Order [LPO].
Precedence:

[U22^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(302) 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.

(303) PisEmptyProof (EQUIVALENT transformation)

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

(304) TRUE

(305) 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.

(306) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(307) 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, 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.

(308) 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)
U21¹(active(X1), X2, X3) → U21¹(X1, X2, X3)
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(x1, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

[U21^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(309) Obligation:

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

U21¹(X1, mark(X2), 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.

(310) 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)

Lexicographic Path Order [LPO].
Precedence:

[U21^1₂, mark₁]

The following usable rules [FROCOS05] were oriented: none

(311) 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.

(312) PisEmptyProof (EQUIVALENT transformation)

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

(313) TRUE

(314) 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.

(315) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(316) 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.

(317) 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: Combined order from the following AFS and order.
ISNELIST(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(318) 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.

(319) PisEmptyProof (EQUIVALENT transformation)

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

(320) TRUE

(321) 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.

(322) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(323) 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.

(324) 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: Combined order from the following AFS and order.
U13¹(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(325) 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.

(326) PisEmptyProof (EQUIVALENT transformation)

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

(327) TRUE

(328) 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.

(329) 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)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(330) 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.

(331) 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: Combined order from the following AFS and order.
ISPALLISTKIND(x1)  =  x1
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(332) 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.

(333) PisEmptyProof (EQUIVALENT transformation)

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

(334) TRUE

(335) 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.

(336) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(337) 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)

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.

(338) 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)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(339) Obligation:

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

U12¹(X1, mark(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.

(340) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(341) 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.

(342) PisEmptyProof (EQUIVALENT transformation)

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

(343) TRUE

(344) 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.

(345) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(346) 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)

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.

U11¹(mark(X1), X2) → U11¹(X1, X2)
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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(348) Obligation:

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

U11¹(X1, mark(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.

(349) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(350) 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.

(351) PisEmptyProof (EQUIVALENT transformation)

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

(352) TRUE

(353) 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.

(354) 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)  =  x2
mark(x1)  =  x1
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(355) 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)

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.

__¹(mark(X1), X2) → __¹(X1, X2)
__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)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(357) Obligation:

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

__¹(X1, mark(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.

(358) 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)  =  x2
mark(x1)  =  mark(x1)

Lexicographic Path Order [LPO].
Precedence:

trivial

The following usable rules [FROCOS05] were oriented: none

(359) 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.

(360) PisEmptyProof (EQUIVALENT transformation)

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

(361) TRUE

(362) 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.

(363) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

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

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
__(x1, x2)  =  __(x1, x2)
ACTIVE(x1)  =  ACTIVE(x1)
mark(x1)  =  x1
U11(x1, x2)  =  U11(x1, x2)
nil  =  nil
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
tt  =  tt
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
active(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u

Lexicographic Path Order [LPO].
Precedence:

[₂, U91₂] > U21₃ > U22₃ > U23₃ > U24₃ > U25₂ > isList₁ > U11₂ > U12₂ > isNeList₁ > U31₂ > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
[₂, U91₂] > U41₃ > U42₃ > U43₃ > U44₃ > isList₁ > U11₂ > U12₂ > isNeList₁ > U31₂ > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
[₂, U91₂] > U41₃ > U42₃ > U43₃ > U44₃ > U45₂ > isNeList₁ > U31₂ > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
[₂, U91₂] > U51₃ > U52₃ > U53₃ > U54₃ > U55₂ > isList₁ > U11₂ > U12₂ > isNeList₁ > U31₂ > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
[₂, U91₂] > U71₃ > U72₂ > isPal₁ > U81₂ > U82₂ > isNePal₁ > U61₂ > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
nil > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
a > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
e > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
i > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
o > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]
u > [tt, U32₂, U62₂] > isQid₁ > [MARK₁, ACTIVE₁, U33₁, U73₂]

The following usable rules [FROCOS05] were oriented:

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

(364) Obligation:

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

MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(U11(X1, X2)) → ACTIVE(U11(mark(X1), X2))
MARK(U12(X1, X2)) → ACTIVE(U12(mark(X1), X2))
MARK(isPalListKind(X)) → ACTIVE(isPalListKind(X))
MARK(U13(X)) → ACTIVE(U13(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(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(U26(X)) → 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(U46(X)) → 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(U56(X)) → 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(U63(X)) → 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(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → ACTIVE(U81(mark(X1), X2))
MARK(U82(X1, X2)) → ACTIVE(U82(mark(X1), X2))
ACTIVE(isPalListKind(__(V1, V2))) → MARK(U91(isPalListKind(V1), V2))
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(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.

(365) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(U13(X)) → ACTIVE(U13(mark(X)))
MARK(U13(X)) → MARK(X)
MARK(U26(X)) → ACTIVE(U26(mark(X)))
MARK(U26(X)) → MARK(X)
MARK(U46(X)) → ACTIVE(U46(mark(X)))
MARK(U46(X)) → MARK(X)
MARK(U56(X)) → ACTIVE(U56(mark(X)))
MARK(U56(X)) → MARK(X)
MARK(U63(X)) → ACTIVE(U63(mark(X)))
MARK(U63(X)) → MARK(X)
MARK(isPal(X)) → ACTIVE(isPal(X))
MARK(U74(X)) → ACTIVE(U74(mark(X)))
MARK(U74(X)) → MARK(X)
MARK(U83(X)) → ACTIVE(U83(mark(X)))
MARK(U83(X)) → MARK(X)
MARK(isNePal(X)) → ACTIVE(isNePal(X))
MARK(U92(X)) → ACTIVE(U92(mark(X)))
MARK(U92(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  x1
__(x1, x2)  =  __
ACTIVE(x1)  =  ACTIVE
mark(x1)  =  mark
U11(x1, x2)  =  U11
U12(x1, x2)  =  U12
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21
U22(x1, x2, x3)  =  U22
U23(x1, x2, x3)  =  U23
U24(x1, x2, x3)  =  U24
U25(x1, x2)  =  U25
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31
U32(x1, x2)  =  U32
U33(x1)  =  U33
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41
U42(x1, x2, x3)  =  U42
U43(x1, x2, x3)  =  U43
U44(x1, x2, x3)  =  U44
U45(x1, x2)  =  U45
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51
U52(x1, x2, x3)  =  U52
U53(x1, x2, x3)  =  U53
U54(x1, x2, x3)  =  U54
U55(x1, x2)  =  U55
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61
U62(x1, x2)  =  U62
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71
U72(x1, x2)  =  U72
U73(x1, x2)  =  U73
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81
U82(x1, x2)  =  U82
U91(x1, x2)  =  U91
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U92(x1)  =  U92(x1)
active(x1)  =  x1
nil  =  nil
tt  =  tt
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u

Lexicographic Path Order [LPO].
Precedence:

_ > [ACTIVE, mark, U11, U12, isPalListKind, U13₁, isNeList, U21, U22, U23, U24, U25, isList, U26₁, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46₁, U51, U52, U53, U54, U55, U56₁, U61, U62, U63₁, U71, U72, U73, U74₁, U81, U82, U91, U83₁, U92₁]
[nil, tt, a, e, i, o, u] > isPal > [ACTIVE, mark, U11, U12, isPalListKind, U13₁, isNeList, U21, U22, U23, U24, U25, isList, U26₁, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46₁, U51, U52, U53, U54, U55, U56₁, U61, U62, U63₁, U71, U72, U73, U74₁, U81, U82, U91, U83₁, U92₁]
[nil, tt, a, e, i, o, u] > isNePal > [ACTIVE, mark, U11, U12, isPalListKind, U13₁, isNeList, U21, U22, U23, U24, U25, isList, U26₁, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46₁, U51, U52, U53, U54, U55, U56₁, U61, U62, U63₁, U71, U72, U73, U74₁, U81, U82, U91, U83₁, U92₁]

The following usable rules [FROCOS05] were oriented:

U91(X1, mark(X2)) → U91(X1, X2)
U91(mark(X1), X2) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)

(366) Obligation:

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

MARK(U11(X1, X2)) → ACTIVE(U11(mark(X1), X2))
MARK(U12(X1, X2)) → ACTIVE(U12(mark(X1), X2))
MARK(isPalListKind(X)) → ACTIVE(isPalListKind(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(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(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(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
MARK(U62(X1, X2)) → ACTIVE(U62(mark(X1), X2))
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(U81(X1, X2)) → ACTIVE(U81(mark(X1), X2))
MARK(U82(X1, X2)) → ACTIVE(U82(mark(X1), X2))
ACTIVE(isPalListKind(__(V1, V2))) → MARK(U91(isPalListKind(V1), V2))
MARK(U91(X1, X2)) → ACTIVE(U91(mark(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.

(367) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U11(X1, X2)) → ACTIVE(U11(mark(X1), X2))
MARK(U12(X1, X2)) → ACTIVE(U12(mark(X1), X2))
MARK(isPalListKind(X)) → ACTIVE(isPalListKind(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(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(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(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
MARK(U62(X1, X2)) → ACTIVE(U62(mark(X1), X2))
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(U81(X1, X2)) → ACTIVE(U81(mark(X1), X2))
MARK(U82(X1, X2)) → ACTIVE(U82(mark(X1), X2))
ACTIVE(isPalListKind(__(V1, V2))) → MARK(U91(isPalListKind(V1), V2))
MARK(U91(X1, X2)) → ACTIVE(U91(mark(X1), X2))

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK(x1)
U11(x1, x2)  =  U11(x2)
ACTIVE(x1)  =  ACTIVE(x1)
mark(x1)  =  mark(x1)
U12(x1, x2)  =  U12
isPalListKind(x1)  =  isPalListKind(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  x3
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32
U33(x1)  =  U33
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  x3
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  x3
U45(x1, x2)  =  U45(x2)
U51(x1, x2, x3)  =  x3
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  U55(x2)
U61(x1, x2)  =  U61(x2)
U62(x1, x2)  =  U62
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  U82
__(x1, x2)  =  __(x1, x2)
U91(x1, x2)  =  U91
active(x1)  =  x1
nil  =  nil
tt  =  tt
U13(x1)  =  U13(x1)
U26(x1)  =  U26(x1)
U46(x1)  =  U46(x1)
U56(x1)  =  U56(x1)
U63(x1)  =  U63
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u

Lexicographic Path Order [LPO].
Precedence:

[MARK₁, ₂] > [U11₁, ACTIVE₁, mark₁, U12, isPalListKind₁, isNeList₁, U25₁, isList₁, U31₁, U32, U33, isQid₁, U45₁, U55₁, U61₁, U62, U72₁, U73, U81₁, U82, U91, U13₁, U26₁, U46₁, U56₁, U63, isPal₁, U74₁, U83₁, U92₁]
[nil, tt, a, e, i, o, u] > isNePal₁ > [U11₁, ACTIVE₁, mark₁, U12, isPalListKind₁, isNeList₁, U25₁, isList₁, U31₁, U32, U33, isQid₁, U45₁, U55₁, U61₁, U62, U72₁, U73, U81₁, U82, U91, U13₁, U26₁, U46₁, U56₁, U63, isPal₁, U74₁, U83₁, U92₁]

The following usable rules [FROCOS05] were oriented:

U11(X1, mark(X2)) → U11(X1, X2)
U11(mark(X1), X2) → U11(X1, X2)
U11(active(X1), X2) → U11(X1, X2)
U11(X1, active(X2)) → U11(X1, X2)
U12(X1, mark(X2)) → U12(X1, X2)
U12(mark(X1), X2) → U12(X1, X2)
U12(active(X1), X2) → U12(X1, X2)
U12(X1, active(X2)) → U12(X1, X2)
isPalListKind(active(X)) → isPalListKind(X)
isPalListKind(mark(X)) → isPalListKind(X)
isNeList(active(X)) → isNeList(X)
isNeList(mark(X)) → isNeList(X)
U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(mark(X1), 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(X1, mark(X2), X3) → U22(X1, X2, X3)
U22(mark(X1), 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(X1, mark(X2), X3) → U23(X1, X2, X3)
U23(mark(X1), 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(X1, mark(X2), X3) → U24(X1, X2, X3)
U24(mark(X1), 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(X1, mark(X2)) → U25(X1, X2)
U25(mark(X1), X2) → U25(X1, X2)
U25(active(X1), X2) → U25(X1, X2)
U25(X1, active(X2)) → U25(X1, X2)
isList(active(X)) → isList(X)
isList(mark(X)) → isList(X)
U31(X1, mark(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(X1, mark(X2)) → U32(X1, X2)
U32(mark(X1), X2) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)
U32(X1, active(X2)) → U32(X1, X2)
U33(active(X)) → U33(X)
U33(mark(X)) → U33(X)
isQid(active(X)) → isQid(X)
isQid(mark(X)) → isQid(X)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(mark(X1), 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(X1, mark(X2), X3) → U42(X1, X2, X3)
U42(mark(X1), 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(X1, mark(X2), X3) → U43(X1, X2, X3)
U43(mark(X1), 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(X1, mark(X2), X3) → U44(X1, X2, X3)
U44(mark(X1), 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(X1, mark(X2)) → U45(X1, X2)
U45(mark(X1), X2) → U45(X1, X2)
U45(active(X1), X2) → U45(X1, X2)
U45(X1, active(X2)) → U45(X1, X2)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(mark(X1), 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(X1, mark(X2), X3) → U52(X1, X2, X3)
U52(mark(X1), 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(X1, mark(X2), X3) → U53(X1, X2, X3)
U53(mark(X1), 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(X1, mark(X2), X3) → U54(X1, X2, X3)
U54(mark(X1), 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(X1, mark(X2)) → U55(X1, X2)
U55(mark(X1), X2) → U55(X1, X2)
U55(active(X1), X2) → U55(X1, X2)
U55(X1, active(X2)) → U55(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(mark(X1), X2) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(X1, mark(X2)) → U62(X1, X2)
U62(mark(X1), X2) → U62(X1, X2)
U62(active(X1), X2) → U62(X1, X2)
U62(X1, active(X2)) → U62(X1, X2)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(mark(X1), 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(X1, mark(X2)) → U72(X1, X2)
U72(mark(X1), X2) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
U73(X1, mark(X2)) → U73(X1, X2)
U73(mark(X1), X2) → U73(X1, X2)
U73(active(X1), X2) → U73(X1, X2)
U73(X1, active(X2)) → U73(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(mark(X1), X2) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(X1, mark(X2)) → U82(X1, X2)
U82(mark(X1), X2) → U82(X1, X2)
U82(active(X1), X2) → U82(X1, X2)
U82(X1, active(X2)) → U82(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(mark(X1), X2) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)

(368) 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.

(369) PisEmptyProof (EQUIVALENT transformation)

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

(370) TRUE