Termination w.r.t. Q of the given QTRS could not be shown:

(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) 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.

(7) 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.

(8) 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.

(9) 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.

(10) 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.

(11) 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.

(12) 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.

(13) 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.

(14) 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.

(15) 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.

(16) 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.

(17) 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.

(18) 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.

(19) 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.

(20) 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.

(21) 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.

(22) 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.

(23) 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.

(24) 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.

(25) 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.

(26) 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.

(27) 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.

(28) 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.

(29) 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.

(30) 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.

(31) 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.

(32) 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.

(33) 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.

(34) 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.

(35) 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.

(36) 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.

(37) 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.

(38) 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.

(39) 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.

(40) 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.

(41) 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.

(42) 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.

(43) 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.

(44) 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.

(45) 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.

(46) 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.

(47) 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.

(48) 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.

(49) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U92(X)) → ACTIVE(U92(mark(X)))

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK
__(x1, x2)  =  __
ACTIVE(x1)  =  x1
mark(x1)  =  mark
U11(x1, x2)  =  U11
nil  =  nil
U12(x1, x2)  =  U12
isPalListKind(x1)  =  isPalListKind
tt  =  tt
U13(x1)  =  U13
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
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
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
U61(x1, x2)  =  U61
U62(x1, x2)  =  U62
U63(x1)  =  U63
U71(x1, x2, x3)  =  U71
U72(x1, x2)  =  U72
U73(x1, x2)  =  U73
isPal(x1)  =  isPal
U74(x1)  =  U74
U81(x1, x2)  =  U81
U82(x1, x2)  =  U82
U83(x1)  =  U83
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91
U92(x1)  =  U92
active(x1)  =  active
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u

Lexicographic path order with status [LPO].
Quasi-Precedence:

tt > [MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U26, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46, U51, U52, U53, U54, U55, U56, U61, U62, U63, U71, U72, U73, isPal, U74, U81, U82, U83, isNePal, U91] > [mark, nil, U92, active] > a
tt > [MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U26, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46, U51, U52, U53, U54, U55, U56, U61, U62, U63, U71, U72, U73, isPal, U74, U81, U82, U83, isNePal, U91] > [mark, nil, U92, active] > e
tt > [MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U26, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46, U51, U52, U53, U54, U55, U56, U61, U62, U63, U71, U72, U73, isPal, U74, U81, U82, U83, isNePal, U91] > [mark, nil, U92, active] > i
tt > [MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U26, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46, U51, U52, U53, U54, U55, U56, U61, U62, U63, U71, U72, U73, isPal, U74, U81, U82, U83, isNePal, U91] > [mark, nil, U92, active] > o
tt > [MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U26, U31, U32, U33, isQid, U41, U42, U43, U44, U45, U46, U51, U52, U53, U54, U55, U56, U61, U62, U63, U71, U72, U73, isPal, U74, U81, U82, U83, isNePal, U91] > [mark, nil, U92, active] > u

Status:

MARK: []
_: []
mark: []
U11: []
nil: []
U12: []
isPalListKind: []
tt: []
U13: []
isNeList: []
U21: []
U22: []
U23: []
U24: []
U25: []
isList: []
U26: []
U31: []
U32: []
U33: []
isQid: []
U41: []
U42: []
U43: []
U44: []
U45: []
U46: []
U51: []
U52: []
U53: []
U54: []
U55: []
U56: []
U61: []
U62: []
U63: []
U71: []
U72: []
U73: []
isPal: []
U74: []
U81: []
U82: []
U83: []
isNePal: []
U91: []
U92: []
active: []
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(50) 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)) → 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.

(51) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U26(X)) → ACTIVE(U26(mark(X)))
MARK(isQid(X)) → ACTIVE(isQid(X))
MARK(U46(X)) → ACTIVE(U46(mark(X)))
MARK(U63(X)) → ACTIVE(U63(mark(X)))
MARK(U74(X)) → ACTIVE(U74(mark(X)))
MARK(U83(X)) → ACTIVE(U83(mark(X)))

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK
__(x1, x2)  =  __
ACTIVE(x1)  =  x1
mark(x1)  =  mark
U11(x1, x2)  =  U11
nil  =  nil
U12(x1, x2)  =  U12
isPalListKind(x1)  =  isPalListKind
tt  =  tt
U13(x1)  =  U13
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
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
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
U61(x1, x2)  =  U61
U62(x1, x2)  =  U62
U63(x1)  =  U63
U71(x1, x2, x3)  =  U71
U72(x1, x2)  =  U72
U73(x1, x2)  =  U73
isPal(x1)  =  isPal
U74(x1)  =  U74
U81(x1, x2)  =  U81
U82(x1, x2)  =  U82
U83(x1)  =  U83
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91
U92(x1)  =  U92
active(x1)  =  active
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u

Lexicographic path order with status [LPO].
Quasi-Precedence:

[MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U33, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U56, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U46 > [tt, U92] > [mark, nil, U26, active, o, u] > e > [isQid, U63, U74]
[MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U33, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U56, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U46 > [tt, U92] > [mark, nil, U26, active, o, u] > i > [isQid, U63, U74]
[MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U33, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U56, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U83 > [tt, U92] > [mark, nil, U26, active, o, u] > e > [isQid, U63, U74]
[MARK, , U11, U12, isPalListKind, U13, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U33, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U56, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U83 > [tt, U92] > [mark, nil, U26, active, o, u] > i > [isQid, U63, U74]
a > [tt, U92] > [mark, nil, U26, active, o, u] > e > [isQid, U63, U74]
a > [tt, U92] > [mark, nil, U26, active, o, u] > i > [isQid, U63, U74]

Status:

MARK: []
_: []
mark: []
U11: []
nil: []
U12: []
isPalListKind: []
tt: []
U13: []
isNeList: []
U21: []
U22: []
U23: []
U24: []
U25: []
isList: []
U26: []
U31: []
U32: []
U33: []
isQid: []
U41: []
U42: []
U43: []
U44: []
U45: []
U46: []
U51: []
U52: []
U53: []
U54: []
U55: []
U56: []
U61: []
U62: []
U63: []
U71: []
U72: []
U73: []
isPal: []
U74: []
U81: []
U82: []
U83: []
isNePal: []
U91: []
U92: []
active: []
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(52) 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)))
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)
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)
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)
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))
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)) → 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)) → 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.

(53) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U13(X)) → ACTIVE(U13(mark(X)))
MARK(U33(X)) → ACTIVE(U33(mark(X)))
MARK(U56(X)) → ACTIVE(U56(mark(X)))

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1)  =  MARK
__(x1, x2)  =  __
ACTIVE(x1)  =  x1
mark(x1)  =  mark
U11(x1, x2)  =  U11
nil  =  nil
U12(x1, x2)  =  U12
isPalListKind(x1)  =  isPalListKind
tt  =  tt
U13(x1)  =  U13
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
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
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
U61(x1, x2)  =  U61
U62(x1, x2)  =  U62
U63(x1)  =  U63
U71(x1, x2, x3)  =  U71
U72(x1, x2)  =  U72
U73(x1, x2)  =  U73
isPal(x1)  =  isPal
U74(x1)  =  U74
U81(x1, x2)  =  U81
U82(x1, x2)  =  U82
U83(x1)  =  U83
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91
U92(x1)  =  U92
active(x1)  =  active
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u

Lexicographic path order with status [LPO].
Quasi-Precedence:

tt > isQid > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U13
tt > isQid > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U26
tt > isQid > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U33
tt > isQid > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U46
tt > isQid > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U56
tt > isQid > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U74
tt > isQid > [mark, nil, U92, active, i] > e
tt > isQid > [mark, nil, U92, active, i] > o
tt > isQid > [mark, nil, U92, active, i] > u
tt > U83 > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U13
tt > U83 > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U26
tt > U83 > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U33
tt > U83 > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U46
tt > U83 > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U56
tt > U83 > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U74
tt > U83 > [mark, nil, U92, active, i] > e
tt > U83 > [mark, nil, U92, active, i] > o
tt > U83 > [mark, nil, U92, active, i] > u
a > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U13
a > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U26
a > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U33
a > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U46
a > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U56
a > [mark, nil, U92, active, i] > U63 > [MARK, , U11, U12, isPalListKind, isNeList, U21, U22, U23, U24, U25, isList, U31, U32, U41, U42, U43, U44, U45, U51, U52, U53, U54, U55, U61, U62, U71, U72, U73, isPal, U81, U82, isNePal, U91] > U74
a > [mark, nil, U92, active, i] > e
a > [mark, nil, U92, active, i] > o
a > [mark, nil, U92, active, i] > u

Status:

MARK: []
_: []
mark: []
U11: []
nil: []
U12: []
isPalListKind: []
tt: []
U13: []
isNeList: []
U21: []
U22: []
U23: []
U24: []
U25: []
isList: []
U26: []
U31: []
U32: []
U33: []
isQid: []
U41: []
U42: []
U43: []
U44: []
U45: []
U46: []
U51: []
U52: []
U53: []
U54: []
U55: []
U56: []
U61: []
U62: []
U63: []
U71: []
U72: []
U73: []
isPal: []
U74: []
U81: []
U82: []
U83: []
isNePal: []
U91: []
U92: []
active: []
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(54) 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))
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)))
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)
ACTIVE(U44(tt, V1, V2)) → MARK(U45(isList(V1), V2))
MARK(U33(X)) → MARK(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)
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)
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)
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))
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)) → 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)) → 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.

(55) 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)))
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))
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(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)
ACTIVE(U44(tt, V1, V2)) → MARK(U45(isList(V1), V2))
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)
ACTIVE(U61(tt, V)) → MARK(U62(isPalListKind(V), V))
MARK(U51(X1, X2, X3)) → ACTIVE(U51(mark(X1), X2, X3))
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)
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(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)
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(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))
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(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)) → MARK(X)
MARK(isNePal(X)) → ACTIVE(isNePal(X))
MARK(U91(X1, X2)) → ACTIVE(U91(mark(X1), X2))
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)  =  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)  =  U13(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)  =  U26(x1)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  x1
isQid(x1)  =  isQid
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)
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)  =  U83(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 with status [LPO].
Quasi-Precedence:

_₂ > U21₃ > U22₃ > U23₃ > U24₃ > U25₂ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U21₃ > U22₃ > U23₃ > U24₃ > U25₂ > U26₁ > U13₁
_₂ > U41₃ > U42₃ > U43₃ > U44₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > U26₁ > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U42₃ > U43₃ > U44₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U53₃ > U54₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U73₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > U83₁ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U51₃ > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > isNePal₁ > U61₂ > [MARK₁, U32₁, U62₁] > U13₁
_₂ > U91₂ > [MARK₁, U32₁, U62₁] > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > U26₁ > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U42₃ > U43₃ > U44₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U53₃ > U54₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U73₂ > [MARK₁, U32₁, U62₁] > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > U83₁ > [MARK₁, U32₁, U62₁] > U13₁
a > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > isNePal₁ > U61₂ > [MARK₁, U32₁, U62₁] > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > U26₁ > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U42₃ > U43₃ > U44₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U53₃ > U54₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U73₂ > [MARK₁, U32₁, U62₁] > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > U83₁ > [MARK₁, U32₁, U62₁] > U13₁
i > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > isNePal₁ > U61₂ > [MARK₁, U32₁, U62₁] > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U22₃ > U23₃ > U24₃ > U25₂ > U26₁ > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U42₃ > U43₃ > U44₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U53₃ > U54₃ > [isList₁, U55₂] > U11₂ > [U12₂, isNeList₁, U45₂] > U31₂ > [MARK₁, U32₁, U62₁] > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U73₂ > [MARK₁, U32₁, U62₁] > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > U83₁ > [MARK₁, U32₁, U62₁] > U13₁
o > [nil, tt, isQid, U52₃, U71₃, U72₂, isPal₁, e, u] > U81₂ > U82₂ > isNePal₁ > U61₂ > [MARK₁, U32₁, U62₁] > U13₁

Status:

MARK₁: [1]
_₂: [1,2]
U11₂: [1,2]
nil: []
U12₂: [2,1]
tt: []
U13₁: [1]
isNeList₁: [1]
U21₃: [2,3,1]
U22₃: [1,3,2]
U23₃: [1,3,2]
U24₃: [1,3,2]
U25₂: [2,1]
isList₁: [1]
U26₁: [1]
U31₂: [1,2]
U32₁: [1]
isQid: []
U41₃: [2,3,1]
U42₃: [3,2,1]
U43₃: [2,3,1]
U44₃: [2,1,3]
U45₂: [2,1]
U51₃: [3,1,2]
U52₃: [1,2,3]
U53₃: [3,2,1]
U54₃: [3,1,2]
U55₂: [2,1]
U61₂: [1,2]
U62₁: [1]
U71₃: [3,2,1]
U72₂: [2,1]
U73₂: [1,2]
isPal₁: [1]
U81₂: [1,2]
U82₂: [1,2]
U83₁: [1]
isNePal₁: [1]
U91₂: [2,1]
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(56) Obligation:

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

ACTIVE(U32(tt, V)) → MARK(U33(isQid(V)))
MARK(U33(X)) → MARK(X)
MARK(U46(X)) → MARK(X)
ACTIVE(U62(tt, V)) → MARK(U63(isQid(V)))
MARK(U56(X)) → MARK(X)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → 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.

(57) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(58) Obligation:

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

MARK(U46(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → 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.

(59) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U56(X)) → MARK(X)

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

Lexicographic path order with status [LPO].
Quasi-Precedence:

_₂ > [tt, isPalListKind, U13, U25, U26, isQid, U72, U73, U83, isNePal, e, i, o, u]
nil > [tt, isPalListKind, U13, U25, U26, isQid, U72, U73, U83, isNePal, e, i, o, u]
[isNeList₁, U41₂, U42₂, U43₂, U44₂, U45₁] > [U51₁, U52₁, U53₁, U54₁] > U55₁ > U56₁ > [tt, isPalListKind, U13, U25, U26, isQid, U72, U73, U83, isNePal, e, i, o, u]
[isNeList₁, U41₂, U42₂, U43₂, U44₂, U45₁] > [U51₁, U52₁, U53₁, U54₁] > U55₁ > [U21₂, isList₁] > U11₁ > [tt, isPalListKind, U13, U25, U26, isQid, U72, U73, U83, isNePal, e, i, o, u]
a > [tt, isPalListKind, U13, U25, U26, isQid, U72, U73, U83, isNePal, e, i, o, u]

Status:

U56₁: [1]
_₂: [1,2]
nil: []
U11₁: [1]
tt: []
isPalListKind: []
U13: []
isNeList₁: [1]
U21₂: [1,2]
U25: []
isList₁: [1]
U26: []
isQid: []
U41₂: [2,1]
U42₂: [2,1]
U43₂: [2,1]
U44₂: [2,1]
U45₁: [1]
U51₁: [1]
U52₁: [1]
U53₁: [1]
U54₁: [1]
U55₁: [1]
U72: []
U73: []
U83: []
isNePal: []
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(60) Obligation:

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

MARK(U46(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → 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.

(61) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U33(X)) → MARK(X)

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

Lexicographic path order with status [LPO].
Quasi-Precedence:

nil > [U33₁, tt, U12, isPalListKind, U13, U22, U25, isList, U32₂, U53₁, U54₁, U55, U56, U73, e, o, u] > U72₁ > isPal₁
[isNeList₁, U41₂, U42₂, U43₂, U44₁, U45₁] > [₂, U51₂] > U52 > [U33₁, tt, U12, isPalListKind, U13, U22, U25, isList, U32₂, U53₁, U54₁, U55, U56, U73, e, o, u] > U72₁ > isPal₁
[isNeList₁, U41₂, U42₂, U43₂, U44₁, U45₁] > [₂, U51₂] > U71₂ > [U33₁, tt, U12, isPalListKind, U13, U22, U25, isList, U32₂, U53₁, U54₁, U55, U56, U73, e, o, u] > U72₁ > isPal₁
[isNeList₁, U41₂, U42₂, U43₂, U44₁, U45₁] > U31₁ > [U33₁, tt, U12, isPalListKind, U13, U22, U25, isList, U32₂, U53₁, U54₁, U55, U56, U73, e, o, u] > U72₁ > isPal₁
a > [U33₁, tt, U12, isPalListKind, U13, U22, U25, isList, U32₂, U53₁, U54₁, U55, U56, U73, e, o, u] > U72₁ > isPal₁
i > [U33₁, tt, U12, isPalListKind, U13, U22, U25, isList, U32₂, U53₁, U54₁, U55, U56, U73, e, o, u] > U72₁ > isPal₁

Status:

U33₁: [1]
_₂: [1,2]
nil: []
tt: []
U12: []
isPalListKind: []
U13: []
isNeList₁: [1]
U22: []
U25: []
isList: []
U31₁: [1]
U32₂: [2,1]
U41₂: [2,1]
U42₂: [2,1]
U43₂: [2,1]
U44₁: [1]
U45₁: [1]
U51₂: [1,2]
U52: []
U53₁: [1]
U54₁: [1]
U55: []
U56: []
U71₂: [2,1]
U72₁: [1]
U73: []
isPal₁: [1]
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(62) Obligation:

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

MARK(U46(X)) → MARK(X)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → 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.

(63) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U46(X)) → MARK(X)
MARK(U74(X)) → MARK(X)

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

Lexicographic path order with status [LPO].
Quasi-Precedence:

_₂ > U41₁ > U42₂ > U43₁ > U44₁ > U45₁ > U46₁ > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
_₂ > U41₁ > U42₂ > U43₁ > U44₁ > U45₁ > [isNeList₁, U31₁, U32] > U33 > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
_₂ > U51₃ > U52₂ > U53₃ > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
_₂ > U71₂ > [U72₁, U73] > U74₁ > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
_₂ > U71₂ > [U72₁, U73] > isPal > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
nil > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
i > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
o > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]
u > [U11, tt, U12, isPalListKind, U13, U24, U25, U26, isQid, U55, U56, U61₁, U83, isNePal₁, a, e]

Status:

U46₁: [1]
U74₁: [1]
_₂: [1,2]
nil: []
U11: []
tt: []
U12: []
isPalListKind: []
U13: []
isNeList₁: [1]
U24: []
U25: []
U26: []
U31₁: [1]
U32: []
U33: []
isQid: []
U41₁: [1]
U42₂: [1,2]
U43₁: [1]
U44₁: [1]
U45₁: [1]
U51₃: [2,3,1]
U52₂: [1,2]
U53₃: [1,3,2]
U55: []
U56: []
U61₁: [1]
U71₂: [1,2]
U72₁: [1]
U73: []
isPal: []
U83: []
isNePal₁: [1]
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(64) Obligation:

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

MARK(U63(X)) → 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.

(65) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U63(X)) → MARK(X)

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

Lexicographic path order with status [LPO].
Quasi-Precedence:

MARK₁ > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
isPal₁ > U81 > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
isNePal > U61 > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
a > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
e > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
i > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
o > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]
u > [U63₁, ₂, nil, tt, isPalListKind, U21₂, U26, U31, isQid, U41₂, U42₂, U43₂, U44₂, U45₁, U46, U54, U55, U56, U62₁, U73, U74, U83, U91]

Status:

MARK₁: [1]
U63₁: [1]
_₂: [1,2]
nil: []
tt: []
isPalListKind: []
U21₂: [1,2]
U26: []
U31: []
isQid: []
U41₂: [1,2]
U42₂: [1,2]
U43₂: [1,2]
U44₂: [1,2]
U45₁: [1]
U46: []
U54: []
U55: []
U56: []
U61: []
U62₁: [1]
U73: []
isPal₁: [1]
U74: []
U81: []
U83: []
isNePal: []
U91: []
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(66) Obligation:

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

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.

(67) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U92(X)) → MARK(X)

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

Lexicographic path order with status [LPO].
Quasi-Precedence:

[₂, U21₂, isList₁, U51₁, U52₁] > U11₂ > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
[₂, U21₂, isList₁, U51₁, U52₁] > U53₁ > U54₁ > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
[₂, U21₂, isList₁, U51₁, U52₁] > U71₁ > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
[₂, U21₂, isList₁, U51₁, U52₁] > U91₂ > U92₁ > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
nil > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
a > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
e > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
i > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]
u > [tt, U13, U22₃, U23₂, U25, U26, isQid, U55, U56, isPal, U74, U81, U82, U83, o]

Status:

U92₁: [1]
_₂: [1,2]
nil: []
U11₂: [1,2]
tt: []
U13: []
U21₂: [1,2]
U22₃: [3,2,1]
U23₂: [2,1]
U25: []
isList₁: [1]
U26: []
isQid: []
U51₁: [1]
U52₁: [1]
U53₁: [1]
U54₁: [1]
U55: []
U56: []
U71₁: [1]
isPal: []
U74: []
U81: []
U82: []
U83: []
U91₂: [1,2]
a: []
e: []
i: []
o: []
u: []

The following usable rules [FROCOS05] were oriented:

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

(68) 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.

(69) PisEmptyProof (EQUIVALENT transformation)

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

(70) TRUE