(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(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)) → __1(X, __(Y, Z))
ACTIVE(__(__(X, Y), Z)) → __1(Y, Z)
ACTIVE(U11(tt, V)) → U121(isPalListKind(V), V)
ACTIVE(U11(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U12(tt, V)) → U131(isNeList(V))
ACTIVE(U12(tt, V)) → ISNELIST(V)
ACTIVE(U21(tt, V1, V2)) → U221(isPalListKind(V1), V1, V2)
ACTIVE(U21(tt, V1, V2)) → ISPALLISTKIND(V1)
ACTIVE(U22(tt, V1, V2)) → U231(isPalListKind(V2), V1, V2)
ACTIVE(U22(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U23(tt, V1, V2)) → U241(isPalListKind(V2), V1, V2)
ACTIVE(U23(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U24(tt, V1, V2)) → U251(isList(V1), V2)
ACTIVE(U24(tt, V1, V2)) → ISLIST(V1)
ACTIVE(U25(tt, V2)) → U261(isList(V2))
ACTIVE(U25(tt, V2)) → ISLIST(V2)
ACTIVE(U31(tt, V)) → U321(isPalListKind(V), V)
ACTIVE(U31(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U32(tt, V)) → U331(isQid(V))
ACTIVE(U32(tt, V)) → ISQID(V)
ACTIVE(U41(tt, V1, V2)) → U421(isPalListKind(V1), V1, V2)
ACTIVE(U41(tt, V1, V2)) → ISPALLISTKIND(V1)
ACTIVE(U42(tt, V1, V2)) → U431(isPalListKind(V2), V1, V2)
ACTIVE(U42(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U43(tt, V1, V2)) → U441(isPalListKind(V2), V1, V2)
ACTIVE(U43(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U44(tt, V1, V2)) → U451(isList(V1), V2)
ACTIVE(U44(tt, V1, V2)) → ISLIST(V1)
ACTIVE(U45(tt, V2)) → U461(isNeList(V2))
ACTIVE(U45(tt, V2)) → ISNELIST(V2)
ACTIVE(U51(tt, V1, V2)) → U521(isPalListKind(V1), V1, V2)
ACTIVE(U51(tt, V1, V2)) → ISPALLISTKIND(V1)
ACTIVE(U52(tt, V1, V2)) → U531(isPalListKind(V2), V1, V2)
ACTIVE(U52(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U53(tt, V1, V2)) → U541(isPalListKind(V2), V1, V2)
ACTIVE(U53(tt, V1, V2)) → ISPALLISTKIND(V2)
ACTIVE(U54(tt, V1, V2)) → U551(isNeList(V1), V2)
ACTIVE(U54(tt, V1, V2)) → ISNELIST(V1)
ACTIVE(U55(tt, V2)) → U561(isList(V2))
ACTIVE(U55(tt, V2)) → ISLIST(V2)
ACTIVE(U61(tt, V)) → U621(isPalListKind(V), V)
ACTIVE(U61(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U62(tt, V)) → U631(isQid(V))
ACTIVE(U62(tt, V)) → ISQID(V)
ACTIVE(U71(tt, I, P)) → U721(isPalListKind(I), P)
ACTIVE(U71(tt, I, P)) → ISPALLISTKIND(I)
ACTIVE(U72(tt, P)) → U731(isPal(P), P)
ACTIVE(U72(tt, P)) → ISPAL(P)
ACTIVE(U73(tt, P)) → U741(isPalListKind(P))
ACTIVE(U73(tt, P)) → ISPALLISTKIND(P)
ACTIVE(U81(tt, V)) → U821(isPalListKind(V), V)
ACTIVE(U81(tt, V)) → ISPALLISTKIND(V)
ACTIVE(U82(tt, V)) → U831(isNePal(V))
ACTIVE(U82(tt, V)) → ISNEPAL(V)
ACTIVE(U91(tt, V2)) → U921(isPalListKind(V2))
ACTIVE(U91(tt, V2)) → ISPALLISTKIND(V2)
ACTIVE(isList(V)) → U111(isPalListKind(V), V)
ACTIVE(isList(V)) → ISPALLISTKIND(V)
ACTIVE(isList(__(V1, V2))) → U211(isPalListKind(V1), V1, V2)
ACTIVE(isList(__(V1, V2))) → ISPALLISTKIND(V1)
ACTIVE(isNeList(V)) → U311(isPalListKind(V), V)
ACTIVE(isNeList(V)) → ISPALLISTKIND(V)
ACTIVE(isNeList(__(V1, V2))) → U411(isPalListKind(V1), V1, V2)
ACTIVE(isNeList(__(V1, V2))) → ISPALLISTKIND(V1)
ACTIVE(isNeList(__(V1, V2))) → U511(isPalListKind(V1), V1, V2)
ACTIVE(isNePal(V)) → U611(isPalListKind(V), V)
ACTIVE(isNePal(V)) → ISPALLISTKIND(V)
ACTIVE(isNePal(__(I, __(P, I)))) → U711(isQid(I), I, P)
ACTIVE(isNePal(__(I, __(P, I)))) → ISQID(I)
ACTIVE(isPal(V)) → U811(isPalListKind(V), V)
ACTIVE(isPal(V)) → ISPALLISTKIND(V)
ACTIVE(isPalListKind(__(V1, V2))) → U911(isPalListKind(V1), V2)
ACTIVE(isPalListKind(__(V1, V2))) → ISPALLISTKIND(V1)
ACTIVE(__(X1, X2)) → __1(active(X1), X2)
ACTIVE(__(X1, X2)) → ACTIVE(X1)
ACTIVE(__(X1, X2)) → __1(X1, active(X2))
ACTIVE(__(X1, X2)) → ACTIVE(X2)
ACTIVE(U11(X1, X2)) → U111(active(X1), X2)
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(X1, X2)) → U121(active(X1), X2)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
ACTIVE(U13(X)) → U131(active(X))
ACTIVE(U13(X)) → ACTIVE(X)
ACTIVE(U21(X1, X2, X3)) → U211(active(X1), X2, X3)
ACTIVE(U21(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U22(X1, X2, X3)) → U221(active(X1), X2, X3)
ACTIVE(U22(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U23(X1, X2, X3)) → U231(active(X1), X2, X3)
ACTIVE(U23(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U24(X1, X2, X3)) → U241(active(X1), X2, X3)
ACTIVE(U24(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U25(X1, X2)) → U251(active(X1), X2)
ACTIVE(U25(X1, X2)) → ACTIVE(X1)
ACTIVE(U26(X)) → U261(active(X))
ACTIVE(U26(X)) → ACTIVE(X)
ACTIVE(U31(X1, X2)) → U311(active(X1), X2)
ACTIVE(U31(X1, X2)) → ACTIVE(X1)
ACTIVE(U32(X1, X2)) → U321(active(X1), X2)
ACTIVE(U32(X1, X2)) → ACTIVE(X1)
ACTIVE(U33(X)) → U331(active(X))
ACTIVE(U33(X)) → ACTIVE(X)
ACTIVE(U41(X1, X2, X3)) → U411(active(X1), X2, X3)
ACTIVE(U41(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U42(X1, X2, X3)) → U421(active(X1), X2, X3)
ACTIVE(U42(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U43(X1, X2, X3)) → U431(active(X1), X2, X3)
ACTIVE(U43(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U44(X1, X2, X3)) → U441(active(X1), X2, X3)
ACTIVE(U44(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U45(X1, X2)) → U451(active(X1), X2)
ACTIVE(U45(X1, X2)) → ACTIVE(X1)
ACTIVE(U46(X)) → U461(active(X))
ACTIVE(U46(X)) → ACTIVE(X)
ACTIVE(U51(X1, X2, X3)) → U511(active(X1), X2, X3)
ACTIVE(U51(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U52(X1, X2, X3)) → U521(active(X1), X2, X3)
ACTIVE(U52(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U53(X1, X2, X3)) → U531(active(X1), X2, X3)
ACTIVE(U53(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U54(X1, X2, X3)) → U541(active(X1), X2, X3)
ACTIVE(U54(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U55(X1, X2)) → U551(active(X1), X2)
ACTIVE(U55(X1, X2)) → ACTIVE(X1)
ACTIVE(U56(X)) → U561(active(X))
ACTIVE(U56(X)) → ACTIVE(X)
ACTIVE(U61(X1, X2)) → U611(active(X1), X2)
ACTIVE(U61(X1, X2)) → ACTIVE(X1)
ACTIVE(U62(X1, X2)) → U621(active(X1), X2)
ACTIVE(U62(X1, X2)) → ACTIVE(X1)
ACTIVE(U63(X)) → U631(active(X))
ACTIVE(U63(X)) → ACTIVE(X)
ACTIVE(U71(X1, X2, X3)) → U711(active(X1), X2, X3)
ACTIVE(U71(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U72(X1, X2)) → U721(active(X1), X2)
ACTIVE(U72(X1, X2)) → ACTIVE(X1)
ACTIVE(U73(X1, X2)) → U731(active(X1), X2)
ACTIVE(U73(X1, X2)) → ACTIVE(X1)
ACTIVE(U74(X)) → U741(active(X))
ACTIVE(U74(X)) → ACTIVE(X)
ACTIVE(U81(X1, X2)) → U811(active(X1), X2)
ACTIVE(U81(X1, X2)) → ACTIVE(X1)
ACTIVE(U82(X1, X2)) → U821(active(X1), X2)
ACTIVE(U82(X1, X2)) → ACTIVE(X1)
ACTIVE(U83(X)) → U831(active(X))
ACTIVE(U83(X)) → ACTIVE(X)
ACTIVE(U91(X1, X2)) → U911(active(X1), X2)
ACTIVE(U91(X1, X2)) → ACTIVE(X1)
ACTIVE(U92(X)) → U921(active(X))
ACTIVE(U92(X)) → ACTIVE(X)
__1(mark(X1), X2) → __1(X1, X2)
__1(X1, mark(X2)) → __1(X1, X2)
U111(mark(X1), X2) → U111(X1, X2)
U121(mark(X1), X2) → U121(X1, X2)
U131(mark(X)) → U131(X)
U211(mark(X1), X2, X3) → U211(X1, X2, X3)
U221(mark(X1), X2, X3) → U221(X1, X2, X3)
U231(mark(X1), X2, X3) → U231(X1, X2, X3)
U241(mark(X1), X2, X3) → U241(X1, X2, X3)
U251(mark(X1), X2) → U251(X1, X2)
U261(mark(X)) → U261(X)
U311(mark(X1), X2) → U311(X1, X2)
U321(mark(X1), X2) → U321(X1, X2)
U331(mark(X)) → U331(X)
U411(mark(X1), X2, X3) → U411(X1, X2, X3)
U421(mark(X1), X2, X3) → U421(X1, X2, X3)
U431(mark(X1), X2, X3) → U431(X1, X2, X3)
U441(mark(X1), X2, X3) → U441(X1, X2, X3)
U451(mark(X1), X2) → U451(X1, X2)
U461(mark(X)) → U461(X)
U511(mark(X1), X2, X3) → U511(X1, X2, X3)
U521(mark(X1), X2, X3) → U521(X1, X2, X3)
U531(mark(X1), X2, X3) → U531(X1, X2, X3)
U541(mark(X1), X2, X3) → U541(X1, X2, X3)
U551(mark(X1), X2) → U551(X1, X2)
U561(mark(X)) → U561(X)
U611(mark(X1), X2) → U611(X1, X2)
U621(mark(X1), X2) → U621(X1, X2)
U631(mark(X)) → U631(X)
U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U721(mark(X1), X2) → U721(X1, X2)
U731(mark(X1), X2) → U731(X1, X2)
U741(mark(X)) → U741(X)
U811(mark(X1), X2) → U811(X1, X2)
U821(mark(X1), X2) → U821(X1, X2)
U831(mark(X)) → U831(X)
U911(mark(X1), X2) → U911(X1, X2)
U921(mark(X)) → U921(X)
PROPER(__(X1, X2)) → __1(proper(X1), proper(X2))
PROPER(__(X1, X2)) → PROPER(X1)
PROPER(__(X1, X2)) → PROPER(X2)
PROPER(U11(X1, X2)) → U111(proper(X1), proper(X2))
PROPER(U11(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X2)
PROPER(U12(X1, X2)) → U121(proper(X1), proper(X2))
PROPER(U12(X1, X2)) → PROPER(X1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(isPalListKind(X)) → ISPALLISTKIND(proper(X))
PROPER(isPalListKind(X)) → PROPER(X)
PROPER(U13(X)) → U131(proper(X))
PROPER(U13(X)) → PROPER(X)
PROPER(isNeList(X)) → ISNELIST(proper(X))
PROPER(isNeList(X)) → PROPER(X)
PROPER(U21(X1, X2, X3)) → U211(proper(X1), proper(X2), proper(X3))
PROPER(U21(X1, X2, X3)) → PROPER(X1)
PROPER(U21(X1, X2, X3)) → PROPER(X2)
PROPER(U21(X1, X2, X3)) → PROPER(X3)
PROPER(U22(X1, X2, X3)) → U221(proper(X1), proper(X2), proper(X3))
PROPER(U22(X1, X2, X3)) → PROPER(X1)
PROPER(U22(X1, X2, X3)) → PROPER(X2)
PROPER(U22(X1, X2, X3)) → PROPER(X3)
PROPER(U23(X1, X2, X3)) → U231(proper(X1), proper(X2), proper(X3))
PROPER(U23(X1, X2, X3)) → PROPER(X1)
PROPER(U23(X1, X2, X3)) → PROPER(X2)
PROPER(U23(X1, X2, X3)) → PROPER(X3)
PROPER(U24(X1, X2, X3)) → U241(proper(X1), proper(X2), proper(X3))
PROPER(U24(X1, X2, X3)) → PROPER(X1)
PROPER(U24(X1, X2, X3)) → PROPER(X2)
PROPER(U24(X1, X2, X3)) → PROPER(X3)
PROPER(U25(X1, X2)) → U251(proper(X1), proper(X2))
PROPER(U25(X1, X2)) → PROPER(X1)
PROPER(U25(X1, X2)) → PROPER(X2)
PROPER(isList(X)) → ISLIST(proper(X))
PROPER(isList(X)) → PROPER(X)
PROPER(U26(X)) → U261(proper(X))
PROPER(U26(X)) → PROPER(X)
PROPER(U31(X1, X2)) → U311(proper(X1), proper(X2))
PROPER(U31(X1, X2)) → PROPER(X1)
PROPER(U31(X1, X2)) → PROPER(X2)
PROPER(U32(X1, X2)) → U321(proper(X1), proper(X2))
PROPER(U32(X1, X2)) → PROPER(X1)
PROPER(U32(X1, X2)) → PROPER(X2)
PROPER(U33(X)) → U331(proper(X))
PROPER(U33(X)) → PROPER(X)
PROPER(isQid(X)) → ISQID(proper(X))
PROPER(isQid(X)) → PROPER(X)
PROPER(U41(X1, X2, X3)) → U411(proper(X1), proper(X2), proper(X3))
PROPER(U41(X1, X2, X3)) → PROPER(X1)
PROPER(U41(X1, X2, X3)) → PROPER(X2)
PROPER(U41(X1, X2, X3)) → PROPER(X3)
PROPER(U42(X1, X2, X3)) → U421(proper(X1), proper(X2), proper(X3))
PROPER(U42(X1, X2, X3)) → PROPER(X1)
PROPER(U42(X1, X2, X3)) → PROPER(X2)
PROPER(U42(X1, X2, X3)) → PROPER(X3)
PROPER(U43(X1, X2, X3)) → U431(proper(X1), proper(X2), proper(X3))
PROPER(U43(X1, X2, X3)) → PROPER(X1)
PROPER(U43(X1, X2, X3)) → PROPER(X2)
PROPER(U43(X1, X2, X3)) → PROPER(X3)
PROPER(U44(X1, X2, X3)) → U441(proper(X1), proper(X2), proper(X3))
PROPER(U44(X1, X2, X3)) → PROPER(X1)
PROPER(U44(X1, X2, X3)) → PROPER(X2)
PROPER(U44(X1, X2, X3)) → PROPER(X3)
PROPER(U45(X1, X2)) → U451(proper(X1), proper(X2))
PROPER(U45(X1, X2)) → PROPER(X1)
PROPER(U45(X1, X2)) → PROPER(X2)
PROPER(U46(X)) → U461(proper(X))
PROPER(U46(X)) → PROPER(X)
PROPER(U51(X1, X2, X3)) → U511(proper(X1), proper(X2), proper(X3))
PROPER(U51(X1, X2, X3)) → PROPER(X1)
PROPER(U51(X1, X2, X3)) → PROPER(X2)
PROPER(U51(X1, X2, X3)) → PROPER(X3)
PROPER(U52(X1, X2, X3)) → U521(proper(X1), proper(X2), proper(X3))
PROPER(U52(X1, X2, X3)) → PROPER(X1)
PROPER(U52(X1, X2, X3)) → PROPER(X2)
PROPER(U52(X1, X2, X3)) → PROPER(X3)
PROPER(U53(X1, X2, X3)) → U531(proper(X1), proper(X2), proper(X3))
PROPER(U53(X1, X2, X3)) → PROPER(X1)
PROPER(U53(X1, X2, X3)) → PROPER(X2)
PROPER(U53(X1, X2, X3)) → PROPER(X3)
PROPER(U54(X1, X2, X3)) → U541(proper(X1), proper(X2), proper(X3))
PROPER(U54(X1, X2, X3)) → PROPER(X1)
PROPER(U54(X1, X2, X3)) → PROPER(X2)
PROPER(U54(X1, X2, X3)) → PROPER(X3)
PROPER(U55(X1, X2)) → U551(proper(X1), proper(X2))
PROPER(U55(X1, X2)) → PROPER(X1)
PROPER(U55(X1, X2)) → PROPER(X2)
PROPER(U56(X)) → U561(proper(X))
PROPER(U56(X)) → PROPER(X)
PROPER(U61(X1, X2)) → U611(proper(X1), proper(X2))
PROPER(U61(X1, X2)) → PROPER(X1)
PROPER(U61(X1, X2)) → PROPER(X2)
PROPER(U62(X1, X2)) → U621(proper(X1), proper(X2))
PROPER(U62(X1, X2)) → PROPER(X1)
PROPER(U62(X1, X2)) → PROPER(X2)
PROPER(U63(X)) → U631(proper(X))
PROPER(U63(X)) → PROPER(X)
PROPER(U71(X1, X2, X3)) → U711(proper(X1), proper(X2), proper(X3))
PROPER(U71(X1, X2, X3)) → PROPER(X1)
PROPER(U71(X1, X2, X3)) → PROPER(X2)
PROPER(U71(X1, X2, X3)) → PROPER(X3)
PROPER(U72(X1, X2)) → U721(proper(X1), proper(X2))
PROPER(U72(X1, X2)) → PROPER(X1)
PROPER(U72(X1, X2)) → PROPER(X2)
PROPER(U73(X1, X2)) → U731(proper(X1), proper(X2))
PROPER(U73(X1, X2)) → PROPER(X1)
PROPER(U73(X1, X2)) → PROPER(X2)
PROPER(isPal(X)) → ISPAL(proper(X))
PROPER(isPal(X)) → PROPER(X)
PROPER(U74(X)) → U741(proper(X))
PROPER(U74(X)) → PROPER(X)
PROPER(U81(X1, X2)) → U811(proper(X1), proper(X2))
PROPER(U81(X1, X2)) → PROPER(X1)
PROPER(U81(X1, X2)) → PROPER(X2)
PROPER(U82(X1, X2)) → U821(proper(X1), proper(X2))
PROPER(U82(X1, X2)) → PROPER(X1)
PROPER(U82(X1, X2)) → PROPER(X2)
PROPER(U83(X)) → U831(proper(X))
PROPER(U83(X)) → PROPER(X)
PROPER(isNePal(X)) → ISNEPAL(proper(X))
PROPER(isNePal(X)) → PROPER(X)
PROPER(U91(X1, X2)) → U911(proper(X1), proper(X2))
PROPER(U91(X1, X2)) → PROPER(X1)
PROPER(U91(X1, X2)) → PROPER(X2)
PROPER(U92(X)) → U921(proper(X))
PROPER(U92(X)) → PROPER(X)
__1(ok(X1), ok(X2)) → __1(X1, X2)
U111(ok(X1), ok(X2)) → U111(X1, X2)
U121(ok(X1), ok(X2)) → U121(X1, X2)
ISPALLISTKIND(ok(X)) → ISPALLISTKIND(X)
U131(ok(X)) → U131(X)
ISNELIST(ok(X)) → ISNELIST(X)
U211(ok(X1), ok(X2), ok(X3)) → U211(X1, X2, X3)
U221(ok(X1), ok(X2), ok(X3)) → U221(X1, X2, X3)
U231(ok(X1), ok(X2), ok(X3)) → U231(X1, X2, X3)
U241(ok(X1), ok(X2), ok(X3)) → U241(X1, X2, X3)
U251(ok(X1), ok(X2)) → U251(X1, X2)
ISLIST(ok(X)) → ISLIST(X)
U261(ok(X)) → U261(X)
U311(ok(X1), ok(X2)) → U311(X1, X2)
U321(ok(X1), ok(X2)) → U321(X1, X2)
U331(ok(X)) → U331(X)
ISQID(ok(X)) → ISQID(X)
U411(ok(X1), ok(X2), ok(X3)) → U411(X1, X2, X3)
U421(ok(X1), ok(X2), ok(X3)) → U421(X1, X2, X3)
U431(ok(X1), ok(X2), ok(X3)) → U431(X1, X2, X3)
U441(ok(X1), ok(X2), ok(X3)) → U441(X1, X2, X3)
U451(ok(X1), ok(X2)) → U451(X1, X2)
U461(ok(X)) → U461(X)
U511(ok(X1), ok(X2), ok(X3)) → U511(X1, X2, X3)
U521(ok(X1), ok(X2), ok(X3)) → U521(X1, X2, X3)
U531(ok(X1), ok(X2), ok(X3)) → U531(X1, X2, X3)
U541(ok(X1), ok(X2), ok(X3)) → U541(X1, X2, X3)
U551(ok(X1), ok(X2)) → U551(X1, X2)
U561(ok(X)) → U561(X)
U611(ok(X1), ok(X2)) → U611(X1, X2)
U621(ok(X1), ok(X2)) → U621(X1, X2)
U631(ok(X)) → U631(X)
U711(ok(X1), ok(X2), ok(X3)) → U711(X1, X2, X3)
U721(ok(X1), ok(X2)) → U721(X1, X2)
U731(ok(X1), ok(X2)) → U731(X1, X2)
ISPAL(ok(X)) → ISPAL(X)
U741(ok(X)) → U741(X)
U811(ok(X1), ok(X2)) → U811(X1, X2)
U821(ok(X1), ok(X2)) → U821(X1, X2)
U831(ok(X)) → U831(X)
ISNEPAL(ok(X)) → ISNEPAL(X)
U911(ok(X1), ok(X2)) → U911(X1, X2)
U921(ok(X)) → U921(X)
TOP(mark(X)) → TOP(proper(X))
TOP(mark(X)) → PROPER(X)
TOP(ok(X)) → TOP(active(X))
TOP(ok(X)) → ACTIVE(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(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 46 SCCs with 156 less nodes.

(4) Complex Obligation (AND)

(5) Obligation:

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

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

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

(6) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(7) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(8) PisEmptyProof (EQUIVALENT transformation)

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

(9) TRUE

(10) Obligation:

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

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

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

(11) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(12) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(13) PisEmptyProof (EQUIVALENT transformation)

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

(14) TRUE

(15) Obligation:

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

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

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

(16) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(17) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(18) PisEmptyProof (EQUIVALENT transformation)

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

(19) TRUE

(20) Obligation:

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

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

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

(21) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(22) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(23) PisEmptyProof (EQUIVALENT transformation)

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

(24) TRUE

(25) Obligation:

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

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

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

(26) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(27) Obligation:

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

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

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

(28) PisEmptyProof (EQUIVALENT transformation)

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

(29) TRUE

(30) Obligation:

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

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

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

(31) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(32) Obligation:

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

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

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

(33) PisEmptyProof (EQUIVALENT transformation)

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

(34) TRUE

(35) Obligation:

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

U921(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(36) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U921(mark(X)) → U921(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U921(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(37) Obligation:

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

U921(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(38) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U921(ok(X)) → U921(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U921(x1)  =  U921(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(39) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(40) PisEmptyProof (EQUIVALENT transformation)

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

(41) TRUE

(42) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(43) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U911(mark(X1), X2) → U911(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U911(x1, x2)  =  U911(x1, x2)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  U52(x1)
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  U74(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)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1 > U91^12
active1 > _2 > isQid
active1 > U131 > mark1 > U91^12
active1 > U131 > tt > isList
active1 > U131 > tt > isNePal1
active1 > isNeList > mark1 > U91^12
active1 > U211 > isPalListKind > mark1 > U91^12
active1 > U211 > isPalListKind > tt > isList
active1 > U211 > isPalListKind > tt > isNePal1
active1 > U211 > U221 > mark1 > U91^12
active1 > U231 > isPalListKind > mark1 > U91^12
active1 > U231 > isPalListKind > tt > isList
active1 > U231 > isPalListKind > tt > isNePal1
active1 > U261 > mark1 > U91^12
active1 > U261 > tt > isList
active1 > U261 > tt > isNePal1
active1 > U311 > mark1 > U91^12
active1 > U411 > isPalListKind > mark1 > U91^12
active1 > U411 > isPalListKind > tt > isList
active1 > U411 > isPalListKind > tt > isNePal1
active1 > U411 > U421 > mark1 > U91^12
active1 > U431 > mark1 > U91^12
active1 > U441 > mark1 > U91^12
active1 > U441 > isList
active1 > U461 > mark1 > U91^12
active1 > U461 > tt > isList
active1 > U461 > tt > isNePal1
active1 > U511 > isPalListKind > mark1 > U91^12
active1 > U511 > isPalListKind > tt > isList
active1 > U511 > isPalListKind > tt > isNePal1
active1 > U511 > U521 > mark1 > U91^12
active1 > U531 > mark1 > U91^12
active1 > U612 > isPalListKind > mark1 > U91^12
active1 > U612 > isPalListKind > tt > isList
active1 > U612 > isPalListKind > tt > isNePal1
active1 > U713 > mark1 > U91^12
active1 > U722 > mark1 > U91^12
active1 > U741 > mark1 > U91^12
active1 > U741 > tt > isList
active1 > U741 > tt > isNePal1
active1 > U812 > mark1 > U91^12
active1 > U822 > mark1 > U91^12
active1 > U822 > isNePal1
active1 > U831 > mark1 > U91^12
active1 > U831 > tt > isList
active1 > U831 > tt > isNePal1
active1 > U911 > isPalListKind > mark1 > U91^12
active1 > U911 > isPalListKind > tt > isList
active1 > U911 > isPalListKind > tt > isNePal1
i > mark1 > U91^12
i > tt > isList
i > tt > isNePal1
o > mark1 > U91^12
o > tt > isList
o > tt > isNePal1

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

(44) Obligation:

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

U911(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(45) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U911(ok(X1), ok(X2)) → U911(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U911(x1, x2)  =  U911(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  x3
U22(x1, x2, x3)  =  U22(x3)
U23(x1, x2, x3)  =  U23(x3)
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  x3
U45(x1, x2)  =  x2
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x2, x3)
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  U82(x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
i > ok1
o > ok1
top > active1 > _2 > isQid1 > ok1
top > active1 > _2 > U512 > U523 > ok1
top > active1 > tt > U131 > ok1
top > active1 > tt > U221 > U231 > ok1
top > active1 > tt > U251 > ok1
top > active1 > tt > isList1 > ok1
top > active1 > tt > U322 > isQid1 > ok1
top > active1 > tt > U423 > ok1
top > active1 > tt > U523 > ok1
top > active1 > tt > U532 > U543 > isNeList1 > ok1
top > active1 > tt > U551 > ok1
top > active1 > tt > U622 > isQid1 > ok1
top > active1 > tt > U721 > U732 > ok1
top > active1 > tt > U821 > ok1
top > active1 > tt > U831 > ok1
top > active1 > tt > isNePal1 > isQid1 > ok1
top > active1 > U311 > U322 > isQid1 > ok1
top > active1 > U413 > U423 > ok1
top > active1 > U712 > U721 > U732 > ok1
top > active1 > U811 > ok1
top > active1 > U912 > ok1
top > proper1 > _2 > isQid1 > ok1
top > proper1 > _2 > U512 > U523 > ok1
top > proper1 > nil > ok1
top > proper1 > U131 > ok1
top > proper1 > U221 > U231 > ok1
top > proper1 > U251 > ok1
top > proper1 > isList1 > ok1
top > proper1 > U311 > U322 > isQid1 > ok1
top > proper1 > U413 > U423 > ok1
top > proper1 > U532 > U543 > isNeList1 > ok1
top > proper1 > U551 > ok1
top > proper1 > U622 > isQid1 > ok1
top > proper1 > U712 > U721 > U732 > ok1
top > proper1 > U811 > ok1
top > proper1 > U821 > ok1
top > proper1 > U831 > ok1
top > proper1 > isNePal1 > isQid1 > ok1
top > proper1 > U912 > ok1
top > proper1 > a > ok1
top > proper1 > e > ok1
top > proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(46) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(47) PisEmptyProof (EQUIVALENT transformation)

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

(48) TRUE

(49) Obligation:

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

U831(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(50) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U831(mark(X)) → U831(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U831(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(51) Obligation:

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

U831(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(52) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U831(ok(X)) → U831(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U831(x1)  =  U831(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(53) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(54) PisEmptyProof (EQUIVALENT transformation)

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

(55) TRUE

(56) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(57) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U821(mark(X1), X2) → U821(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U821(x1, x2)  =  U821(x1, x2)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  U45(x1)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  U55(x1)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1)
U62(x1, x2)  =  U62(x1)
U63(x1)  =  x1
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  x1
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1)
U82(x1, x2)  =  x1
U83(x1)  =  x1
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U211 > mark1
active1 > _2 > U411 > U421 > mark1
active1 > _2 > U511 > mark1
active1 > _2 > U911 > mark1
active1 > tt > isNeList > U311 > mark1
active1 > tt > U221 > U231 > mark1
active1 > tt > U321 > U331 > mark1
active1 > tt > U421 > mark1
active1 > tt > U431 > mark1
active1 > tt > U441 > U451 > U461 > mark1
active1 > tt > U531 > mark1
active1 > tt > U551 > mark1
active1 > tt > U561 > mark1
active1 > tt > U621 > mark1
active1 > tt > isPal > U811 > mark1
active1 > isPalListKind > U911 > mark1
active1 > isList > U211 > mark1
active1 > isQid > mark1
active1 > isNePal > U611 > mark1
nil > tt > isNeList > U311 > mark1
nil > tt > U221 > U231 > mark1
nil > tt > U321 > U331 > mark1
nil > tt > U421 > mark1
nil > tt > U431 > mark1
nil > tt > U441 > U451 > U461 > mark1
nil > tt > U531 > mark1
nil > tt > U551 > mark1
nil > tt > U561 > mark1
nil > tt > U621 > mark1
nil > tt > isPal > U811 > mark1
a > tt > isNeList > U311 > mark1
a > tt > U221 > U231 > mark1
a > tt > U321 > U331 > mark1
a > tt > U421 > mark1
a > tt > U431 > mark1
a > tt > U441 > U451 > U461 > mark1
a > tt > U531 > mark1
a > tt > U551 > mark1
a > tt > U561 > mark1
a > tt > U621 > mark1
a > tt > isPal > U811 > mark1
i > tt > isNeList > U311 > mark1
i > tt > U221 > U231 > mark1
i > tt > U321 > U331 > mark1
i > tt > U421 > mark1
i > tt > U431 > mark1
i > tt > U441 > U451 > U461 > mark1
i > tt > U531 > mark1
i > tt > U551 > mark1
i > tt > U561 > mark1
i > tt > U621 > mark1
i > tt > isPal > U811 > mark1
o > mark1
u > mark1

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

(58) Obligation:

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

U821(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(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.


U821(ok(X1), ok(X2)) → U821(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U821(x1, x2)  =  U821(x2)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1)
mark(x1)  =  mark
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x3)
U22(x1, x2, x3)  =  U22(x2)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x3)
U42(x1, x2, x3)  =  x2
U43(x1, x2, x3)  =  x2
U44(x1, x2, x3)  =  U44(x1, x2)
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  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)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U82^11 > mark
i > ok1 > mark
i > tt > mark
u > ok1 > mark
u > tt > mark
proper1 > nil > mark
proper1 > U221 > active1 > _1 > U212 > ok1 > mark
proper1 > U221 > active1 > _1 > U412 > ok1 > mark
proper1 > U221 > active1 > U131 > ok1 > mark
proper1 > U221 > active1 > U131 > tt > mark
proper1 > U221 > active1 > U233 > ok1 > mark
proper1 > U221 > active1 > U252 > isList1 > U112 > ok1 > mark
proper1 > U221 > active1 > U252 > isList1 > tt > mark
proper1 > U221 > active1 > U252 > isList1 > U212 > ok1 > mark
proper1 > U221 > active1 > U322 > ok1 > mark
proper1 > U221 > active1 > isQid1 > ok1 > mark
proper1 > U221 > active1 > isQid1 > tt > mark
proper1 > U221 > active1 > U442 > isList1 > U112 > ok1 > mark
proper1 > U221 > active1 > U442 > isList1 > tt > mark
proper1 > U221 > active1 > U442 > isList1 > U212 > ok1 > mark
proper1 > U221 > active1 > U461 > ok1 > mark
proper1 > U221 > active1 > U461 > tt > mark
proper1 > U221 > active1 > U523 > ok1 > mark
proper1 > U221 > active1 > U533 > U543 > ok1 > mark
proper1 > U221 > active1 > U612 > ok1 > mark
proper1 > U221 > active1 > U631 > ok1 > mark
proper1 > U221 > active1 > U631 > tt > mark
proper1 > U221 > active1 > U721 > ok1 > mark
proper1 > U221 > active1 > U812 > ok1 > mark
proper1 > U221 > active1 > U831 > ok1 > mark
proper1 > U221 > active1 > U831 > tt > mark
proper1 > U221 > active1 > U921 > ok1 > mark
proper1 > U221 > active1 > U921 > tt > mark
proper1 > U221 > isPalListKind1 > ok1 > mark
proper1 > U221 > isPalListKind1 > tt > mark
proper1 > U311 > active1 > _1 > U212 > ok1 > mark
proper1 > U311 > active1 > _1 > U412 > ok1 > mark
proper1 > U311 > active1 > U131 > ok1 > mark
proper1 > U311 > active1 > U131 > tt > mark
proper1 > U311 > active1 > U233 > ok1 > mark
proper1 > U311 > active1 > U252 > isList1 > U112 > ok1 > mark
proper1 > U311 > active1 > U252 > isList1 > tt > mark
proper1 > U311 > active1 > U252 > isList1 > U212 > ok1 > mark
proper1 > U311 > active1 > U322 > ok1 > mark
proper1 > U311 > active1 > isQid1 > ok1 > mark
proper1 > U311 > active1 > isQid1 > tt > mark
proper1 > U311 > active1 > U442 > isList1 > U112 > ok1 > mark
proper1 > U311 > active1 > U442 > isList1 > tt > mark
proper1 > U311 > active1 > U442 > isList1 > U212 > ok1 > mark
proper1 > U311 > active1 > U461 > ok1 > mark
proper1 > U311 > active1 > U461 > tt > mark
proper1 > U311 > active1 > U523 > ok1 > mark
proper1 > U311 > active1 > U533 > U543 > ok1 > mark
proper1 > U311 > active1 > U612 > ok1 > mark
proper1 > U311 > active1 > U631 > ok1 > mark
proper1 > U311 > active1 > U631 > tt > mark
proper1 > U311 > active1 > U721 > ok1 > mark
proper1 > U311 > active1 > U812 > ok1 > mark
proper1 > U311 > active1 > U831 > ok1 > mark
proper1 > U311 > active1 > U831 > tt > mark
proper1 > U311 > active1 > U921 > ok1 > mark
proper1 > U311 > active1 > U921 > tt > mark
proper1 > U311 > isPalListKind1 > ok1 > mark
proper1 > U311 > isPalListKind1 > tt > mark
proper1 > U731 > active1 > _1 > U212 > ok1 > mark
proper1 > U731 > active1 > _1 > U412 > ok1 > mark
proper1 > U731 > active1 > U131 > ok1 > mark
proper1 > U731 > active1 > U131 > tt > mark
proper1 > U731 > active1 > U233 > ok1 > mark
proper1 > U731 > active1 > U252 > isList1 > U112 > ok1 > mark
proper1 > U731 > active1 > U252 > isList1 > tt > mark
proper1 > U731 > active1 > U252 > isList1 > U212 > ok1 > mark
proper1 > U731 > active1 > U322 > ok1 > mark
proper1 > U731 > active1 > isQid1 > ok1 > mark
proper1 > U731 > active1 > isQid1 > tt > mark
proper1 > U731 > active1 > U442 > isList1 > U112 > ok1 > mark
proper1 > U731 > active1 > U442 > isList1 > tt > mark
proper1 > U731 > active1 > U442 > isList1 > U212 > ok1 > mark
proper1 > U731 > active1 > U461 > ok1 > mark
proper1 > U731 > active1 > U461 > tt > mark
proper1 > U731 > active1 > U523 > ok1 > mark
proper1 > U731 > active1 > U533 > U543 > ok1 > mark
proper1 > U731 > active1 > U612 > ok1 > mark
proper1 > U731 > active1 > U631 > ok1 > mark
proper1 > U731 > active1 > U631 > tt > mark
proper1 > U731 > active1 > U721 > ok1 > mark
proper1 > U731 > active1 > U812 > ok1 > mark
proper1 > U731 > active1 > U831 > ok1 > mark
proper1 > U731 > active1 > U831 > tt > mark
proper1 > U731 > active1 > U921 > ok1 > mark
proper1 > U731 > active1 > U921 > tt > mark
proper1 > U731 > isPalListKind1 > ok1 > mark
proper1 > U731 > isPalListKind1 > tt > mark
proper1 > a > mark
proper1 > e > tt > mark
proper1 > o > tt > mark
top > mark

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

(60) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(61) PisEmptyProof (EQUIVALENT transformation)

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

(62) TRUE

(63) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(64) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U811(ok(X1), ok(X2)) → U811(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U811(x1, x2)  =  x1
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x3)
U23(x1, x2, x3)  =  U23(x1, x3)
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  x2
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  x2
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x2, x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  x3
U45(x1, x2)  =  x2
U46(x1)  =  x1
U51(x1, x2, x3)  =  x3
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  U53(x1, x3)
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U213 > ok1
active1 > U112 > ok1
active1 > U131 > ok1
active1 > U131 > tt
active1 > isNeList1 > ok1
active1 > U222 > ok1
active1 > U232 > ok1
active1 > isList1 > ok1
active1 > isList1 > tt
active1 > isQid1 > ok1
active1 > isQid1 > tt
active1 > U413 > U422 > ok1
active1 > U532 > ok1
active1 > U631 > ok1
active1 > U631 > tt
active1 > U721 > isPal1 > ok1
active1 > U721 > isPal1 > tt
active1 > U732 > ok1
active1 > U741 > ok1
active1 > U741 > tt
active1 > U831 > ok1
active1 > U831 > tt
active1 > isNePal1 > ok1
active1 > U912 > ok1
proper1 > _2 > U213 > ok1
proper1 > nil > tt
proper1 > U112 > ok1
proper1 > U131 > ok1
proper1 > U131 > tt
proper1 > isNeList1 > ok1
proper1 > U222 > ok1
proper1 > U232 > ok1
proper1 > isList1 > ok1
proper1 > isList1 > tt
proper1 > isQid1 > ok1
proper1 > isQid1 > tt
proper1 > U413 > U422 > ok1
proper1 > U532 > ok1
proper1 > U631 > ok1
proper1 > U631 > tt
proper1 > U721 > isPal1 > ok1
proper1 > U721 > isPal1 > tt
proper1 > U732 > ok1
proper1 > U741 > ok1
proper1 > U741 > tt
proper1 > U831 > ok1
proper1 > U831 > tt
proper1 > isNePal1 > ok1
proper1 > U912 > ok1
proper1 > a
proper1 > e > ok1
proper1 > e > tt
proper1 > i
proper1 > o
proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(65) Obligation:

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

U811(mark(X1), X2) → U811(X1, X2)

The TRS R consists of the following rules:

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

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

(66) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U811(mark(X1), X2) → U811(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U811(x1, x2)  =  U811(x1)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  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)
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  x1
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U81^11 > mark1
top > active1 > _2 > U413 > ok > U433 > mark1
top > active1 > _2 > U413 > ok > U513 > mark1
top > active1 > _2 > U413 > ok > U523 > U533 > mark1
top > active1 > _2 > U911 > mark1
top > active1 > U112 > U122 > ok > U433 > mark1
top > active1 > U112 > U122 > ok > U513 > mark1
top > active1 > U112 > U122 > ok > U523 > U533 > mark1
top > active1 > U131 > tt > mark1
top > active1 > U131 > ok > U433 > mark1
top > active1 > U131 > ok > U513 > mark1
top > active1 > U131 > ok > U523 > U533 > mark1
top > active1 > U213 > isPalListKind > tt > mark1
top > active1 > U213 > isPalListKind > U911 > mark1
top > active1 > U213 > isPalListKind > ok > U433 > mark1
top > active1 > U213 > isPalListKind > ok > U513 > mark1
top > active1 > U213 > isPalListKind > ok > U523 > U533 > mark1
top > active1 > U223 > isPalListKind > tt > mark1
top > active1 > U223 > isPalListKind > U911 > mark1
top > active1 > U223 > isPalListKind > ok > U433 > mark1
top > active1 > U223 > isPalListKind > ok > U513 > mark1
top > active1 > U223 > isPalListKind > ok > U523 > U533 > mark1
top > active1 > U233 > isPalListKind > tt > mark1
top > active1 > U233 > isPalListKind > U911 > mark1
top > active1 > U233 > isPalListKind > ok > U433 > mark1
top > active1 > U233 > isPalListKind > ok > U513 > mark1
top > active1 > U233 > isPalListKind > ok > U523 > U533 > mark1
top > active1 > U243 > U252 > ok > U433 > mark1
top > active1 > U243 > U252 > ok > U513 > mark1
top > active1 > U243 > U252 > ok > U523 > U533 > mark1
top > active1 > isQid > tt > mark1
top > active1 > isQid > ok > U433 > mark1
top > active1 > isQid > ok > U513 > mark1
top > active1 > isQid > ok > U523 > U533 > mark1
top > active1 > U423 > isPalListKind > tt > mark1
top > active1 > U423 > isPalListKind > U911 > mark1
top > active1 > U423 > isPalListKind > ok > U433 > mark1
top > active1 > U423 > isPalListKind > ok > U513 > mark1
top > active1 > U423 > isPalListKind > ok > U523 > U533 > mark1
top > active1 > U443 > U452 > ok > U433 > mark1
top > active1 > U443 > U452 > ok > U513 > mark1
top > active1 > U443 > U452 > ok > U523 > U533 > mark1
top > active1 > U543 > ok > U433 > mark1
top > active1 > U543 > ok > U513 > mark1
top > active1 > U543 > ok > U523 > U533 > mark1
top > active1 > U552 > ok > U433 > mark1
top > active1 > U552 > ok > U513 > mark1
top > active1 > U552 > ok > U523 > U533 > mark1
top > active1 > U721 > isPal > tt > mark1
top > active1 > U721 > isPal > ok > U433 > mark1
top > active1 > U721 > isPal > ok > U513 > mark1
top > active1 > U721 > isPal > ok > U523 > U533 > mark1
top > active1 > U741 > tt > mark1
top > active1 > U741 > ok > U433 > mark1
top > active1 > U741 > ok > U513 > mark1
top > active1 > U741 > ok > U523 > U533 > mark1
top > active1 > isNePal > U611 > ok > U433 > mark1
top > active1 > isNePal > U611 > ok > U513 > mark1
top > active1 > isNePal > U611 > ok > U523 > U533 > mark1
top > proper1 > _2 > U413 > ok > U433 > mark1
top > proper1 > _2 > U413 > ok > U513 > mark1
top > proper1 > _2 > U413 > ok > U523 > U533 > mark1
top > proper1 > _2 > U911 > mark1
top > proper1 > nil > mark1
top > proper1 > U112 > U122 > ok > U433 > mark1
top > proper1 > U112 > U122 > ok > U513 > mark1
top > proper1 > U112 > U122 > ok > U523 > U533 > mark1
top > proper1 > U131 > tt > mark1
top > proper1 > U131 > ok > U433 > mark1
top > proper1 > U131 > ok > U513 > mark1
top > proper1 > U131 > ok > U523 > U533 > mark1
top > proper1 > U213 > isPalListKind > tt > mark1
top > proper1 > U213 > isPalListKind > U911 > mark1
top > proper1 > U213 > isPalListKind > ok > U433 > mark1
top > proper1 > U213 > isPalListKind > ok > U513 > mark1
top > proper1 > U213 > isPalListKind > ok > U523 > U533 > mark1
top > proper1 > U223 > isPalListKind > tt > mark1
top > proper1 > U223 > isPalListKind > U911 > mark1
top > proper1 > U223 > isPalListKind > ok > U433 > mark1
top > proper1 > U223 > isPalListKind > ok > U513 > mark1
top > proper1 > U223 > isPalListKind > ok > U523 > U533 > mark1
top > proper1 > U233 > isPalListKind > tt > mark1
top > proper1 > U233 > isPalListKind > U911 > mark1
top > proper1 > U233 > isPalListKind > ok > U433 > mark1
top > proper1 > U233 > isPalListKind > ok > U513 > mark1
top > proper1 > U233 > isPalListKind > ok > U523 > U533 > mark1
top > proper1 > U243 > U252 > ok > U433 > mark1
top > proper1 > U243 > U252 > ok > U513 > mark1
top > proper1 > U243 > U252 > ok > U523 > U533 > mark1
top > proper1 > isQid > tt > mark1
top > proper1 > isQid > ok > U433 > mark1
top > proper1 > isQid > ok > U513 > mark1
top > proper1 > isQid > ok > U523 > U533 > mark1
top > proper1 > U423 > isPalListKind > tt > mark1
top > proper1 > U423 > isPalListKind > U911 > mark1
top > proper1 > U423 > isPalListKind > ok > U433 > mark1
top > proper1 > U423 > isPalListKind > ok > U513 > mark1
top > proper1 > U423 > isPalListKind > ok > U523 > U533 > mark1
top > proper1 > U443 > U452 > ok > U433 > mark1
top > proper1 > U443 > U452 > ok > U513 > mark1
top > proper1 > U443 > U452 > ok > U523 > U533 > mark1
top > proper1 > U543 > ok > U433 > mark1
top > proper1 > U543 > ok > U513 > mark1
top > proper1 > U543 > ok > U523 > U533 > mark1
top > proper1 > U552 > ok > U433 > mark1
top > proper1 > U552 > ok > U513 > mark1
top > proper1 > U552 > ok > U523 > U533 > mark1
top > proper1 > U721 > isPal > tt > mark1
top > proper1 > U721 > isPal > ok > U433 > mark1
top > proper1 > U721 > isPal > ok > U513 > mark1
top > proper1 > U721 > isPal > ok > U523 > U533 > mark1
top > proper1 > U741 > tt > mark1
top > proper1 > U741 > ok > U433 > mark1
top > proper1 > U741 > ok > U513 > mark1
top > proper1 > U741 > ok > U523 > U533 > mark1
top > proper1 > isNePal > U611 > ok > U433 > mark1
top > proper1 > isNePal > U611 > ok > U513 > mark1
top > proper1 > isNePal > U611 > ok > U523 > U533 > mark1
top > proper1 > a > mark1
top > proper1 > e > tt > mark1
top > proper1 > e > ok > U433 > mark1
top > proper1 > e > ok > U513 > mark1
top > proper1 > e > ok > U523 > U533 > mark1
top > proper1 > i > tt > mark1
top > proper1 > i > ok > U433 > mark1
top > proper1 > i > ok > U513 > mark1
top > proper1 > i > ok > U523 > U533 > mark1
top > proper1 > o > tt > mark1
top > proper1 > o > ok > U433 > mark1
top > proper1 > o > ok > U513 > mark1
top > proper1 > o > ok > U523 > U533 > mark1
top > proper1 > u > mark1

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

(67) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(68) PisEmptyProof (EQUIVALENT transformation)

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

(69) TRUE

(70) Obligation:

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

U741(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(71) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U741(mark(X)) → U741(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U741(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(72) Obligation:

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

U741(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(73) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U741(ok(X)) → U741(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U741(x1)  =  U741(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(74) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(75) PisEmptyProof (EQUIVALENT transformation)

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

(76) TRUE

(77) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(78) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U731(mark(X1), X2) → U731(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U731(x1, x2)  =  U731(x1)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  U55(x1)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U73^11 > mark1
active1 > _2 > U911 > mark1
active1 > isPalListKind > tt > U631 > mark1
active1 > isPalListKind > tt > U822 > mark1
active1 > isPalListKind > U911 > mark1
active1 > U131 > tt > U631 > mark1
active1 > U131 > tt > U822 > mark1
active1 > U221 > mark1
active1 > U231 > mark1
active1 > U241 > isList > U111 > mark1
active1 > U241 > isList > tt > U631 > mark1
active1 > U241 > isList > tt > U822 > mark1
active1 > U251 > isList > U111 > mark1
active1 > U251 > isList > tt > U631 > mark1
active1 > U251 > isList > tt > U822 > mark1
active1 > U261 > tt > U631 > mark1
active1 > U261 > tt > U822 > mark1
active1 > U321 > mark1
active1 > U331 > tt > U631 > mark1
active1 > U331 > tt > U822 > mark1
active1 > U441 > U451 > isNeList > mark1
active1 > U531 > mark1
active1 > U541 > isNeList > mark1
active1 > U541 > U551 > mark1
active1 > U612 > mark1
active1 > U622 > isQid > tt > U631 > mark1
active1 > U622 > isQid > tt > U822 > mark1
active1 > U712 > U722 > mark1
active1 > U812 > U822 > mark1
active1 > U831 > tt > U631 > mark1
active1 > U831 > tt > U822 > mark1
i > tt > U631 > mark1
i > tt > U822 > mark1
proper1 > _2 > U911 > mark1
proper1 > nil > mark1
proper1 > isPalListKind > tt > U631 > mark1
proper1 > isPalListKind > tt > U822 > mark1
proper1 > isPalListKind > U911 > mark1
proper1 > U131 > tt > U631 > mark1
proper1 > U131 > tt > U822 > mark1
proper1 > U221 > mark1
proper1 > U231 > mark1
proper1 > U241 > isList > U111 > mark1
proper1 > U241 > isList > tt > U631 > mark1
proper1 > U241 > isList > tt > U822 > mark1
proper1 > U251 > isList > U111 > mark1
proper1 > U251 > isList > tt > U631 > mark1
proper1 > U251 > isList > tt > U822 > mark1
proper1 > U261 > tt > U631 > mark1
proper1 > U261 > tt > U822 > mark1
proper1 > U321 > mark1
proper1 > U331 > tt > U631 > mark1
proper1 > U331 > tt > U822 > mark1
proper1 > U441 > U451 > isNeList > mark1
proper1 > U531 > mark1
proper1 > U541 > isNeList > mark1
proper1 > U541 > U551 > mark1
proper1 > U612 > mark1
proper1 > U622 > isQid > tt > U631 > mark1
proper1 > U622 > isQid > tt > U822 > mark1
proper1 > U712 > U722 > mark1
proper1 > U812 > U822 > mark1
proper1 > U831 > tt > U631 > mark1
proper1 > U831 > tt > U822 > mark1
proper1 > a > mark1
proper1 > e > tt > U631 > mark1
proper1 > e > tt > U822 > mark1
proper1 > o > tt > U631 > mark1
proper1 > o > tt > U822 > mark1
proper1 > u > tt > U631 > mark1
proper1 > u > tt > U822 > mark1
top > mark1

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

(79) Obligation:

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

U731(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(80) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U731(ok(X1), ok(X2)) → U731(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U731(x1, x2)  =  U731(x1, x2)
ok(x1)  =  ok(x1)
active(x1)  =  x1
__(x1, x2)  =  x2
mark(x1)  =  mark
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  U23(x2)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x2
U32(x1, x2)  =  U32(x1)
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x2)
U53(x1, x2, x3)  =  x2
U54(x1, x2, x3)  =  x2
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  x1
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U73^12 > mark
proper1 > nil > mark
proper1 > tt > U121 > ok1 > mark
proper1 > tt > isPalListKind1 > ok1 > mark
proper1 > tt > U131 > ok1 > mark
proper1 > tt > U231 > ok1 > mark
proper1 > tt > U241 > U252 > ok1 > mark
proper1 > tt > U321 > isQid1 > ok1 > mark
proper1 > tt > U423 > ok1 > mark
proper1 > tt > U443 > ok1 > mark
proper1 > tt > U452 > ok1 > mark
proper1 > tt > U461 > ok1 > mark
proper1 > tt > U521 > ok1 > mark
proper1 > tt > U552 > U561 > ok1 > mark
proper1 > tt > U621 > isQid1 > ok1 > mark
proper1 > tt > U631 > ok1 > mark
proper1 > tt > U731 > ok1 > mark
proper1 > tt > isPal1 > ok1 > mark
proper1 > tt > U741 > ok1 > mark
proper1 > tt > U921 > ok1 > mark
proper1 > U213 > ok1 > mark
proper1 > U413 > isPalListKind1 > ok1 > mark
proper1 > U413 > U423 > ok1 > mark
proper1 > U512 > isPalListKind1 > ok1 > mark
proper1 > U512 > U521 > ok1 > mark
proper1 > U612 > isPalListKind1 > ok1 > mark
proper1 > U612 > U621 > isQid1 > ok1 > mark
proper1 > U721 > U731 > ok1 > mark
proper1 > U721 > isPal1 > ok1 > mark
proper1 > U812 > ok1 > mark
proper1 > a > mark
proper1 > e > ok1 > mark
proper1 > i > ok1 > mark
proper1 > o > mark
proper1 > u > ok1 > mark
top > mark

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

(81) Obligation:

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

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

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

(82) PisEmptyProof (EQUIVALENT transformation)

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

(83) TRUE

(84) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(85) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U721(mark(X1), X2) → U721(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U721(x1, x2)  =  U721(x1, x2)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  U55(x1)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  x1
U62(x1, x2)  =  U62(x1)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > isPalListKind > proper1 > _2 > mark1
active1 > isPalListKind > proper1 > U111 > mark1
active1 > isPalListKind > proper1 > U131 > mark1
active1 > isPalListKind > proper1 > U131 > tt > isList
active1 > isPalListKind > proper1 > U211 > U221 > mark1
active1 > isPalListKind > proper1 > U241 > mark1
active1 > isPalListKind > proper1 > U241 > isList
active1 > isPalListKind > proper1 > U261 > mark1
active1 > isPalListKind > proper1 > U261 > tt > isList
active1 > isPalListKind > proper1 > U311 > U321 > mark1
active1 > isPalListKind > proper1 > U331 > mark1
active1 > isPalListKind > proper1 > U331 > tt > isList
active1 > isPalListKind > proper1 > U421 > mark1
active1 > isPalListKind > proper1 > U431 > mark1
active1 > isPalListKind > proper1 > U441 > mark1
active1 > isPalListKind > proper1 > U441 > isList
active1 > isPalListKind > proper1 > U461 > mark1
active1 > isPalListKind > proper1 > U461 > tt > isList
active1 > isPalListKind > proper1 > U511 > mark1
active1 > isPalListKind > proper1 > U531 > mark1
active1 > isPalListKind > proper1 > U541 > isNeList
active1 > isPalListKind > proper1 > U541 > U551 > mark1
active1 > isPalListKind > proper1 > U541 > U551 > isList
active1 > isPalListKind > proper1 > U561 > mark1
active1 > isPalListKind > proper1 > U561 > tt > isList
active1 > isPalListKind > proper1 > U621 > mark1
active1 > isPalListKind > proper1 > U711 > mark1
active1 > isPalListKind > proper1 > U741 > mark1
active1 > isPalListKind > proper1 > U741 > tt > isList
active1 > isPalListKind > proper1 > U831 > mark1
active1 > isPalListKind > proper1 > U831 > tt > isList
active1 > isPalListKind > proper1 > U911 > U921 > mark1
active1 > isPalListKind > proper1 > U911 > U921 > tt > isList
active1 > isPalListKind > proper1 > i
active1 > isPalListKind > proper1 > o > mark1
active1 > isPalListKind > proper1 > o > tt > isList
active1 > isPal > proper1 > _2 > mark1
active1 > isPal > proper1 > U111 > mark1
active1 > isPal > proper1 > U131 > mark1
active1 > isPal > proper1 > U131 > tt > isList
active1 > isPal > proper1 > U211 > U221 > mark1
active1 > isPal > proper1 > U241 > mark1
active1 > isPal > proper1 > U241 > isList
active1 > isPal > proper1 > U261 > mark1
active1 > isPal > proper1 > U261 > tt > isList
active1 > isPal > proper1 > U311 > U321 > mark1
active1 > isPal > proper1 > U331 > mark1
active1 > isPal > proper1 > U331 > tt > isList
active1 > isPal > proper1 > U421 > mark1
active1 > isPal > proper1 > U431 > mark1
active1 > isPal > proper1 > U441 > mark1
active1 > isPal > proper1 > U441 > isList
active1 > isPal > proper1 > U461 > mark1
active1 > isPal > proper1 > U461 > tt > isList
active1 > isPal > proper1 > U511 > mark1
active1 > isPal > proper1 > U531 > mark1
active1 > isPal > proper1 > U541 > isNeList
active1 > isPal > proper1 > U541 > U551 > mark1
active1 > isPal > proper1 > U541 > U551 > isList
active1 > isPal > proper1 > U561 > mark1
active1 > isPal > proper1 > U561 > tt > isList
active1 > isPal > proper1 > U621 > mark1
active1 > isPal > proper1 > U711 > mark1
active1 > isPal > proper1 > U741 > mark1
active1 > isPal > proper1 > U741 > tt > isList
active1 > isPal > proper1 > U831 > mark1
active1 > isPal > proper1 > U831 > tt > isList
active1 > isPal > proper1 > U911 > U921 > mark1
active1 > isPal > proper1 > U911 > U921 > tt > isList
active1 > isPal > proper1 > i
active1 > isPal > proper1 > o > mark1
active1 > isPal > proper1 > o > tt > isList
active1 > isNePal > isQid > proper1 > _2 > mark1
active1 > isNePal > isQid > proper1 > U111 > mark1
active1 > isNePal > isQid > proper1 > U131 > mark1
active1 > isNePal > isQid > proper1 > U131 > tt > isList
active1 > isNePal > isQid > proper1 > U211 > U221 > mark1
active1 > isNePal > isQid > proper1 > U241 > mark1
active1 > isNePal > isQid > proper1 > U241 > isList
active1 > isNePal > isQid > proper1 > U261 > mark1
active1 > isNePal > isQid > proper1 > U261 > tt > isList
active1 > isNePal > isQid > proper1 > U311 > U321 > mark1
active1 > isNePal > isQid > proper1 > U331 > mark1
active1 > isNePal > isQid > proper1 > U331 > tt > isList
active1 > isNePal > isQid > proper1 > U421 > mark1
active1 > isNePal > isQid > proper1 > U431 > mark1
active1 > isNePal > isQid > proper1 > U441 > mark1
active1 > isNePal > isQid > proper1 > U441 > isList
active1 > isNePal > isQid > proper1 > U461 > mark1
active1 > isNePal > isQid > proper1 > U461 > tt > isList
active1 > isNePal > isQid > proper1 > U511 > mark1
active1 > isNePal > isQid > proper1 > U531 > mark1
active1 > isNePal > isQid > proper1 > U541 > isNeList
active1 > isNePal > isQid > proper1 > U541 > U551 > mark1
active1 > isNePal > isQid > proper1 > U541 > U551 > isList
active1 > isNePal > isQid > proper1 > U561 > mark1
active1 > isNePal > isQid > proper1 > U561 > tt > isList
active1 > isNePal > isQid > proper1 > U621 > mark1
active1 > isNePal > isQid > proper1 > U711 > mark1
active1 > isNePal > isQid > proper1 > U741 > mark1
active1 > isNePal > isQid > proper1 > U741 > tt > isList
active1 > isNePal > isQid > proper1 > U831 > mark1
active1 > isNePal > isQid > proper1 > U831 > tt > isList
active1 > isNePal > isQid > proper1 > U911 > U921 > mark1
active1 > isNePal > isQid > proper1 > U911 > U921 > tt > isList
active1 > isNePal > isQid > proper1 > i
active1 > isNePal > isQid > proper1 > o > mark1
active1 > isNePal > isQid > proper1 > o > tt > isList
nil > mark1
nil > tt > isList
a > mark1
a > tt > isList
e > mark1
e > tt > isList
u > mark1
u > tt > isList
top > proper1 > _2 > mark1
top > proper1 > U111 > mark1
top > proper1 > U131 > mark1
top > proper1 > U131 > tt > isList
top > proper1 > U211 > U221 > mark1
top > proper1 > U241 > mark1
top > proper1 > U241 > isList
top > proper1 > U261 > mark1
top > proper1 > U261 > tt > isList
top > proper1 > U311 > U321 > mark1
top > proper1 > U331 > mark1
top > proper1 > U331 > tt > isList
top > proper1 > U421 > mark1
top > proper1 > U431 > mark1
top > proper1 > U441 > mark1
top > proper1 > U441 > isList
top > proper1 > U461 > mark1
top > proper1 > U461 > tt > isList
top > proper1 > U511 > mark1
top > proper1 > U531 > mark1
top > proper1 > U541 > isNeList
top > proper1 > U541 > U551 > mark1
top > proper1 > U541 > U551 > isList
top > proper1 > U561 > mark1
top > proper1 > U561 > tt > isList
top > proper1 > U621 > mark1
top > proper1 > U711 > mark1
top > proper1 > U741 > mark1
top > proper1 > U741 > tt > isList
top > proper1 > U831 > mark1
top > proper1 > U831 > tt > isList
top > proper1 > U911 > U921 > mark1
top > proper1 > U911 > U921 > tt > isList
top > proper1 > i
top > proper1 > o > mark1
top > proper1 > o > tt > isList

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

(86) Obligation:

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

U721(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(87) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U721(ok(X1), ok(X2)) → U721(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U721(x1, x2)  =  U721(x2)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
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)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U72^11 > ok1
active1 > _2 > U213 > mark1 > ok1
active1 > _2 > U513 > U523 > mark1 > ok1
active1 > _2 > U713 > U722 > mark1 > ok1
active1 > _2 > U912 > mark1 > ok1
active1 > U112 > U122 > mark1 > ok1
active1 > tt > U122 > mark1 > ok1
active1 > tt > U131 > mark1 > ok1
active1 > tt > isNeList1 > isPalListKind1 > U912 > mark1 > ok1
active1 > tt > isNeList1 > U312 > U322 > mark1 > ok1
active1 > tt > isNeList1 > U513 > U523 > mark1 > ok1
active1 > tt > U223 > isPalListKind1 > U912 > mark1 > ok1
active1 > tt > U233 > isPalListKind1 > U912 > mark1 > ok1
active1 > tt > U233 > U243 > mark1 > ok1
active1 > tt > U252 > U261 > mark1 > ok1
active1 > tt > U423 > mark1 > ok1
active1 > tt > U433 > U443 > mark1 > ok1
active1 > tt > U452 > mark1 > ok1
active1 > tt > U533 > mark1 > ok1
active1 > tt > U543 > U552 > mark1 > ok1
active1 > tt > U622 > mark1 > ok1
active1 > tt > U722 > mark1 > ok1
active1 > tt > U732 > U741 > mark1 > ok1
active1 > tt > U822 > mark1 > ok1
active1 > tt > U921 > mark1 > ok1
active1 > U413 > isPalListKind1 > U912 > mark1 > ok1
active1 > U413 > U423 > mark1 > ok1
active1 > U612 > isPalListKind1 > U912 > mark1 > ok1
active1 > U812 > mark1 > ok1
nil > mark1 > ok1
i > mark1 > ok1
proper1 > _2 > U213 > mark1 > ok1
proper1 > _2 > U513 > U523 > mark1 > ok1
proper1 > _2 > U713 > U722 > mark1 > ok1
proper1 > _2 > U912 > mark1 > ok1
proper1 > U112 > U122 > mark1 > ok1
proper1 > U131 > mark1 > ok1
proper1 > isNeList1 > isPalListKind1 > U912 > mark1 > ok1
proper1 > isNeList1 > U312 > U322 > mark1 > ok1
proper1 > isNeList1 > U513 > U523 > mark1 > ok1
proper1 > U223 > isPalListKind1 > U912 > mark1 > ok1
proper1 > U233 > isPalListKind1 > U912 > mark1 > ok1
proper1 > U233 > U243 > mark1 > ok1
proper1 > U252 > U261 > mark1 > ok1
proper1 > U413 > isPalListKind1 > U912 > mark1 > ok1
proper1 > U413 > U423 > mark1 > ok1
proper1 > U433 > U443 > mark1 > ok1
proper1 > U452 > mark1 > ok1
proper1 > U533 > mark1 > ok1
proper1 > U543 > U552 > mark1 > ok1
proper1 > U612 > isPalListKind1 > U912 > mark1 > ok1
proper1 > U622 > mark1 > ok1
proper1 > U732 > U741 > mark1 > ok1
proper1 > U812 > mark1 > ok1
proper1 > U822 > mark1 > ok1
proper1 > U921 > mark1 > ok1
proper1 > a > mark1 > ok1
proper1 > e > ok1
proper1 > o > ok1
proper1 > u > mark1 > ok1
top > ok1

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

(88) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(89) PisEmptyProof (EQUIVALENT transformation)

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

(90) TRUE

(91) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(92) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(ok(X1), ok(X2), ok(X3)) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  U711(x1, x2, x3)
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x2)
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
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(x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, 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)  =  x2
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
i > tt > U223 > ok1 > U71^13
i > tt > U252 > ok1 > U71^13
i > tt > U322 > ok1 > U71^13
i > tt > U422 > ok1 > U71^13
i > tt > U442 > ok1 > U71^13
i > tt > U542 > isNeList1 > ok1 > U71^13
i > tt > U721 > ok1 > U71^13
i > tt > U831 > ok1 > U71^13
top > active1 > _2 > ok1 > U71^13
top > active1 > U111 > ok1 > U71^13
top > active1 > U131 > tt > U223 > ok1 > U71^13
top > active1 > U131 > tt > U252 > ok1 > U71^13
top > active1 > U131 > tt > U322 > ok1 > U71^13
top > active1 > U131 > tt > U422 > ok1 > U71^13
top > active1 > U131 > tt > U442 > ok1 > U71^13
top > active1 > U131 > tt > U542 > isNeList1 > ok1 > U71^13
top > active1 > U131 > tt > U721 > ok1 > U71^13
top > active1 > U131 > tt > U831 > ok1 > U71^13
top > active1 > U213 > U223 > ok1 > U71^13
top > active1 > U233 > ok1 > U71^13
top > active1 > U242 > U252 > ok1 > U71^13
top > active1 > isList1 > tt > U223 > ok1 > U71^13
top > active1 > isList1 > tt > U252 > ok1 > U71^13
top > active1 > isList1 > tt > U322 > ok1 > U71^13
top > active1 > isList1 > tt > U422 > ok1 > U71^13
top > active1 > isList1 > tt > U442 > ok1 > U71^13
top > active1 > isList1 > tt > U542 > isNeList1 > ok1 > U71^13
top > active1 > isList1 > tt > U721 > ok1 > U71^13
top > active1 > isList1 > tt > U831 > ok1 > U71^13
top > active1 > U311 > U322 > ok1 > U71^13
top > active1 > U413 > U422 > ok1 > U71^13
top > active1 > U432 > U442 > ok1 > U71^13
top > active1 > U512 > ok1 > U71^13
top > active1 > U523 > ok1 > U71^13
top > active1 > U631 > tt > U223 > ok1 > U71^13
top > active1 > U631 > tt > U252 > ok1 > U71^13
top > active1 > U631 > tt > U322 > ok1 > U71^13
top > active1 > U631 > tt > U422 > ok1 > U71^13
top > active1 > U631 > tt > U442 > ok1 > U71^13
top > active1 > U631 > tt > U542 > isNeList1 > ok1 > U71^13
top > active1 > U631 > tt > U721 > ok1 > U71^13
top > active1 > U631 > tt > U831 > ok1 > U71^13
top > active1 > U731 > ok1 > U71^13
top > active1 > U741 > tt > U223 > ok1 > U71^13
top > active1 > U741 > tt > U252 > ok1 > U71^13
top > active1 > U741 > tt > U322 > ok1 > U71^13
top > active1 > U741 > tt > U422 > ok1 > U71^13
top > active1 > U741 > tt > U442 > ok1 > U71^13
top > active1 > U741 > tt > U542 > isNeList1 > ok1 > U71^13
top > active1 > U741 > tt > U721 > ok1 > U71^13
top > active1 > U741 > tt > U831 > ok1 > U71^13
top > proper1 > _2 > ok1 > U71^13
top > proper1 > nil > U71^13
top > proper1 > U111 > ok1 > U71^13
top > proper1 > U131 > tt > U223 > ok1 > U71^13
top > proper1 > U131 > tt > U252 > ok1 > U71^13
top > proper1 > U131 > tt > U322 > ok1 > U71^13
top > proper1 > U131 > tt > U422 > ok1 > U71^13
top > proper1 > U131 > tt > U442 > ok1 > U71^13
top > proper1 > U131 > tt > U542 > isNeList1 > ok1 > U71^13
top > proper1 > U131 > tt > U721 > ok1 > U71^13
top > proper1 > U131 > tt > U831 > ok1 > U71^13
top > proper1 > U213 > U223 > ok1 > U71^13
top > proper1 > U233 > ok1 > U71^13
top > proper1 > U242 > U252 > ok1 > U71^13
top > proper1 > isList1 > tt > U223 > ok1 > U71^13
top > proper1 > isList1 > tt > U252 > ok1 > U71^13
top > proper1 > isList1 > tt > U322 > ok1 > U71^13
top > proper1 > isList1 > tt > U422 > ok1 > U71^13
top > proper1 > isList1 > tt > U442 > ok1 > U71^13
top > proper1 > isList1 > tt > U542 > isNeList1 > ok1 > U71^13
top > proper1 > isList1 > tt > U721 > ok1 > U71^13
top > proper1 > isList1 > tt > U831 > ok1 > U71^13
top > proper1 > U311 > U322 > ok1 > U71^13
top > proper1 > U413 > U422 > ok1 > U71^13
top > proper1 > U432 > U442 > ok1 > U71^13
top > proper1 > U512 > ok1 > U71^13
top > proper1 > U523 > ok1 > U71^13
top > proper1 > U631 > tt > U223 > ok1 > U71^13
top > proper1 > U631 > tt > U252 > ok1 > U71^13
top > proper1 > U631 > tt > U322 > ok1 > U71^13
top > proper1 > U631 > tt > U422 > ok1 > U71^13
top > proper1 > U631 > tt > U442 > ok1 > U71^13
top > proper1 > U631 > tt > U542 > isNeList1 > ok1 > U71^13
top > proper1 > U631 > tt > U721 > ok1 > U71^13
top > proper1 > U631 > tt > U831 > ok1 > U71^13
top > proper1 > U731 > ok1 > U71^13
top > proper1 > isPal1 > tt > U223 > ok1 > U71^13
top > proper1 > isPal1 > tt > U252 > ok1 > U71^13
top > proper1 > isPal1 > tt > U322 > ok1 > U71^13
top > proper1 > isPal1 > tt > U422 > ok1 > U71^13
top > proper1 > isPal1 > tt > U442 > ok1 > U71^13
top > proper1 > isPal1 > tt > U542 > isNeList1 > ok1 > U71^13
top > proper1 > isPal1 > tt > U721 > ok1 > U71^13
top > proper1 > isPal1 > tt > U831 > ok1 > U71^13
top > proper1 > U741 > tt > U223 > ok1 > U71^13
top > proper1 > U741 > tt > U252 > ok1 > U71^13
top > proper1 > U741 > tt > U322 > ok1 > U71^13
top > proper1 > U741 > tt > U422 > ok1 > U71^13
top > proper1 > U741 > tt > U442 > ok1 > U71^13
top > proper1 > U741 > tt > U542 > isNeList1 > ok1 > U71^13
top > proper1 > U741 > tt > U721 > ok1 > U71^13
top > proper1 > U741 > tt > U831 > ok1 > U71^13
top > proper1 > a > ok1 > U71^13
top > proper1 > e > ok1 > U71^13
top > proper1 > o > ok1 > U71^13
top > proper1 > u > ok1 > U71^13

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

(93) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(94) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U711(mark(X1), X2, X3) → U711(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U711(x1, x2, x3)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1 > ok
active1 > _2 > isQid > tt > ok
active1 > U111 > U121 > mark1 > ok
active1 > U111 > isPalListKind > mark1 > ok
active1 > U111 > isPalListKind > tt > ok
active1 > U131 > mark1 > ok
active1 > U131 > tt > ok
active1 > U231 > U241 > mark1 > ok
active1 > U231 > U241 > isList > tt > ok
active1 > U251 > mark1 > ok
active1 > U251 > isList > tt > ok
active1 > U261 > mark1 > ok
active1 > U261 > tt > ok
active1 > U451 > isNeList > U311 > mark1 > ok
active1 > U531 > mark1 > ok
active1 > U711 > isPalListKind > mark1 > ok
active1 > U711 > isPalListKind > tt > ok
active1 > U731 > U741 > mark1 > ok
active1 > U731 > U741 > tt > ok
active1 > isPal > tt > ok
active1 > U831 > mark1 > ok
active1 > U831 > tt > ok
active1 > isNePal > isPalListKind > mark1 > ok
active1 > isNePal > isPalListKind > tt > ok
active1 > isNePal > isQid > tt > ok
active1 > U911 > mark1 > ok
nil > ok
a > ok
e > ok
i > ok
o > ok
u > tt > ok
top > ok

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

(95) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(96) PisEmptyProof (EQUIVALENT transformation)

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

(97) TRUE

(98) Obligation:

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

U631(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(99) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U631(mark(X)) → U631(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U631(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(100) Obligation:

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

U631(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(101) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U631(ok(X)) → U631(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U631(x1)  =  U631(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(102) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(103) PisEmptyProof (EQUIVALENT transformation)

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

(104) TRUE

(105) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(106) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U621(mark(X1), X2) → U621(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U621(x1, x2)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(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)  =  U56(x1)
U61(x1, x2)  =  x1
U62(x1, x2)  =  U62(x1)
U63(x1)  =  x1
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  x1
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U122 > U131 > tt > U252 > mark1
active1 > U122 > U131 > tt > U331 > mark1
active1 > U122 > U131 > tt > U423 > mark1
active1 > U122 > U131 > tt > U452 > mark1
active1 > U122 > U131 > tt > U543 > mark1
active1 > U122 > U131 > tt > U731 > mark1
active1 > U213 > isPalListKind > tt > U252 > mark1
active1 > U213 > isPalListKind > tt > U331 > mark1
active1 > U213 > isPalListKind > tt > U423 > mark1
active1 > U213 > isPalListKind > tt > U452 > mark1
active1 > U213 > isPalListKind > tt > U543 > mark1
active1 > U213 > isPalListKind > tt > U731 > mark1
active1 > U213 > U223 > mark1
active1 > U233 > mark1
active1 > U243 > U252 > mark1
active1 > U261 > tt > U252 > mark1
active1 > U261 > tt > U331 > mark1
active1 > U261 > tt > U423 > mark1
active1 > U261 > tt > U452 > mark1
active1 > U261 > tt > U543 > mark1
active1 > U261 > tt > U731 > mark1
active1 > U311 > U321 > U331 > mark1
active1 > isQid > tt > U252 > mark1
active1 > isQid > tt > U331 > mark1
active1 > isQid > tt > U423 > mark1
active1 > isQid > tt > U452 > mark1
active1 > isQid > tt > U543 > mark1
active1 > isQid > tt > U731 > mark1
active1 > U413 > U423 > mark1
active1 > U433 > U443 > U452 > mark1
active1 > U513 > mark1
active1 > U523 > U533 > U543 > mark1
active1 > U552 > mark1
active1 > U561 > tt > U252 > mark1
active1 > U561 > tt > U331 > mark1
active1 > U561 > tt > U423 > mark1
active1 > U561 > tt > U452 > mark1
active1 > U561 > tt > U543 > mark1
active1 > U561 > tt > U731 > mark1
active1 > U621 > mark1
active1 > isPal > tt > U252 > mark1
active1 > isPal > tt > U331 > mark1
active1 > isPal > tt > U423 > mark1
active1 > isPal > tt > U452 > mark1
active1 > isPal > tt > U543 > mark1
active1 > isPal > tt > U731 > mark1
active1 > U741 > tt > U252 > mark1
active1 > U741 > tt > U331 > mark1
active1 > U741 > tt > U423 > mark1
active1 > U741 > tt > U452 > mark1
active1 > U741 > tt > U543 > mark1
active1 > U741 > tt > U731 > mark1
active1 > U831 > tt > U252 > mark1
active1 > U831 > tt > U331 > mark1
active1 > U831 > tt > U423 > mark1
active1 > U831 > tt > U452 > mark1
active1 > U831 > tt > U543 > mark1
active1 > U831 > tt > U731 > mark1
active1 > isNePal > mark1
nil > tt > U252 > mark1
nil > tt > U331 > mark1
nil > tt > U423 > mark1
nil > tt > U452 > mark1
nil > tt > U543 > mark1
nil > tt > U731 > mark1
a > tt > U252 > mark1
a > tt > U331 > mark1
a > tt > U423 > mark1
a > tt > U452 > mark1
a > tt > U543 > mark1
a > tt > U731 > mark1
e > tt > U252 > mark1
e > tt > U331 > mark1
e > tt > U423 > mark1
e > tt > U452 > mark1
e > tt > U543 > mark1
e > tt > U731 > mark1
i > tt > U252 > mark1
i > tt > U331 > mark1
i > tt > U423 > mark1
i > tt > U452 > mark1
i > tt > U543 > mark1
i > tt > U731 > mark1
o > tt > U252 > mark1
o > tt > U331 > mark1
o > tt > U423 > mark1
o > tt > U452 > mark1
o > tt > U543 > mark1
o > tt > U731 > mark1
u > mark1
top > mark1

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

(107) Obligation:

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

U621(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(108) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U621(ok(X1), ok(X2)) → U621(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U621(x1, x2)  =  U621(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
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)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(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)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U213 > ok1
active1 > _2 > U213 > mark1
active1 > _2 > U413 > U423 > ok1
active1 > _2 > U413 > U423 > mark1
active1 > _2 > U713 > ok1
active1 > _2 > U713 > mark1
active1 > _2 > U912 > ok1
active1 > _2 > U912 > mark1
active1 > U112 > U122 > ok1
active1 > U112 > U122 > mark1
active1 > U131 > tt > U122 > ok1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > isNeList1 > U413 > U423 > ok1
active1 > U131 > tt > isNeList1 > U413 > U423 > mark1
active1 > U131 > tt > U223 > U233 > U243 > ok1
active1 > U131 > tt > U223 > U233 > U243 > mark1
active1 > U131 > tt > U261 > ok1
active1 > U131 > tt > U261 > mark1
active1 > U131 > tt > U322 > ok1
active1 > U131 > tt > U322 > mark1
active1 > U131 > tt > U452 > U461 > ok1
active1 > U131 > tt > U452 > U461 > mark1
active1 > U131 > tt > U543 > U552 > ok1
active1 > U131 > tt > U543 > U552 > mark1
active1 > U131 > tt > U622 > ok1
active1 > U131 > tt > U622 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U722 > isPal1 > ok1
active1 > U131 > tt > U741 > ok1
active1 > U131 > tt > U741 > mark1
active1 > U252 > U261 > ok1
active1 > U252 > U261 > mark1
active1 > U312 > U322 > ok1
active1 > U312 > U322 > mark1
active1 > U433 > ok1
active1 > U433 > mark1
active1 > U443 > U452 > U461 > ok1
active1 > U443 > U452 > U461 > mark1
active1 > U513 > ok1
active1 > U513 > mark1
active1 > U523 > ok1
active1 > U523 > mark1
active1 > U533 > U543 > U552 > ok1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > ok1
active1 > U612 > mark1
active1 > U631 > tt > U122 > ok1
active1 > U631 > tt > U122 > mark1
active1 > U631 > tt > isNeList1 > U413 > U423 > ok1
active1 > U631 > tt > isNeList1 > U413 > U423 > mark1
active1 > U631 > tt > U223 > U233 > U243 > ok1
active1 > U631 > tt > U223 > U233 > U243 > mark1
active1 > U631 > tt > U261 > ok1
active1 > U631 > tt > U261 > mark1
active1 > U631 > tt > U322 > ok1
active1 > U631 > tt > U322 > mark1
active1 > U631 > tt > U452 > U461 > ok1
active1 > U631 > tt > U452 > U461 > mark1
active1 > U631 > tt > U543 > U552 > ok1
active1 > U631 > tt > U543 > U552 > mark1
active1 > U631 > tt > U622 > ok1
active1 > U631 > tt > U622 > mark1
active1 > U631 > tt > U722 > mark1
active1 > U631 > tt > U722 > isPal1 > ok1
active1 > U631 > tt > U741 > ok1
active1 > U631 > tt > U741 > mark1
active1 > U732 > U741 > ok1
active1 > U732 > U741 > mark1
active1 > U812 > ok1
active1 > U812 > mark1
active1 > U822 > U831 > tt > U122 > ok1
active1 > U822 > U831 > tt > U122 > mark1
active1 > U822 > U831 > tt > isNeList1 > U413 > U423 > ok1
active1 > U822 > U831 > tt > isNeList1 > U413 > U423 > mark1
active1 > U822 > U831 > tt > U223 > U233 > U243 > ok1
active1 > U822 > U831 > tt > U223 > U233 > U243 > mark1
active1 > U822 > U831 > tt > U261 > ok1
active1 > U822 > U831 > tt > U261 > mark1
active1 > U822 > U831 > tt > U322 > ok1
active1 > U822 > U831 > tt > U322 > mark1
active1 > U822 > U831 > tt > U452 > U461 > ok1
active1 > U822 > U831 > tt > U452 > U461 > mark1
active1 > U822 > U831 > tt > U543 > U552 > ok1
active1 > U822 > U831 > tt > U543 > U552 > mark1
active1 > U822 > U831 > tt > U622 > ok1
active1 > U822 > U831 > tt > U622 > mark1
active1 > U822 > U831 > tt > U722 > mark1
active1 > U822 > U831 > tt > U722 > isPal1 > ok1
active1 > U822 > U831 > tt > U741 > ok1
active1 > U822 > U831 > tt > U741 > mark1
e > tt > U122 > ok1
e > tt > U122 > mark1
e > tt > isNeList1 > U413 > U423 > ok1
e > tt > isNeList1 > U413 > U423 > mark1
e > tt > U223 > U233 > U243 > ok1
e > tt > U223 > U233 > U243 > mark1
e > tt > U261 > ok1
e > tt > U261 > mark1
e > tt > U322 > ok1
e > tt > U322 > mark1
e > tt > U452 > U461 > ok1
e > tt > U452 > U461 > mark1
e > tt > U543 > U552 > ok1
e > tt > U543 > U552 > mark1
e > tt > U622 > ok1
e > tt > U622 > mark1
e > tt > U722 > mark1
e > tt > U722 > isPal1 > ok1
e > tt > U741 > ok1
e > tt > U741 > mark1
proper1 > _2 > U213 > ok1
proper1 > _2 > U213 > mark1
proper1 > _2 > U413 > U423 > ok1
proper1 > _2 > U413 > U423 > mark1
proper1 > _2 > U713 > ok1
proper1 > _2 > U713 > mark1
proper1 > _2 > U912 > ok1
proper1 > _2 > U912 > mark1
proper1 > nil > ok1
proper1 > nil > mark1
proper1 > U112 > U122 > ok1
proper1 > U112 > U122 > mark1
proper1 > U131 > tt > U122 > ok1
proper1 > U131 > tt > U122 > mark1
proper1 > U131 > tt > isNeList1 > U413 > U423 > ok1
proper1 > U131 > tt > isNeList1 > U413 > U423 > mark1
proper1 > U131 > tt > U223 > U233 > U243 > ok1
proper1 > U131 > tt > U223 > U233 > U243 > mark1
proper1 > U131 > tt > U261 > ok1
proper1 > U131 > tt > U261 > mark1
proper1 > U131 > tt > U322 > ok1
proper1 > U131 > tt > U322 > mark1
proper1 > U131 > tt > U452 > U461 > ok1
proper1 > U131 > tt > U452 > U461 > mark1
proper1 > U131 > tt > U543 > U552 > ok1
proper1 > U131 > tt > U543 > U552 > mark1
proper1 > U131 > tt > U622 > ok1
proper1 > U131 > tt > U622 > mark1
proper1 > U131 > tt > U722 > mark1
proper1 > U131 > tt > U722 > isPal1 > ok1
proper1 > U131 > tt > U741 > ok1
proper1 > U131 > tt > U741 > mark1
proper1 > U252 > U261 > ok1
proper1 > U252 > U261 > mark1
proper1 > U312 > U322 > ok1
proper1 > U312 > U322 > mark1
proper1 > U433 > ok1
proper1 > U433 > mark1
proper1 > U443 > U452 > U461 > ok1
proper1 > U443 > U452 > U461 > mark1
proper1 > U513 > ok1
proper1 > U513 > mark1
proper1 > U523 > ok1
proper1 > U523 > mark1
proper1 > U533 > U543 > U552 > ok1
proper1 > U533 > U543 > U552 > mark1
proper1 > U612 > ok1
proper1 > U612 > mark1
proper1 > U631 > tt > U122 > ok1
proper1 > U631 > tt > U122 > mark1
proper1 > U631 > tt > isNeList1 > U413 > U423 > ok1
proper1 > U631 > tt > isNeList1 > U413 > U423 > mark1
proper1 > U631 > tt > U223 > U233 > U243 > ok1
proper1 > U631 > tt > U223 > U233 > U243 > mark1
proper1 > U631 > tt > U261 > ok1
proper1 > U631 > tt > U261 > mark1
proper1 > U631 > tt > U322 > ok1
proper1 > U631 > tt > U322 > mark1
proper1 > U631 > tt > U452 > U461 > ok1
proper1 > U631 > tt > U452 > U461 > mark1
proper1 > U631 > tt > U543 > U552 > ok1
proper1 > U631 > tt > U543 > U552 > mark1
proper1 > U631 > tt > U622 > ok1
proper1 > U631 > tt > U622 > mark1
proper1 > U631 > tt > U722 > mark1
proper1 > U631 > tt > U722 > isPal1 > ok1
proper1 > U631 > tt > U741 > ok1
proper1 > U631 > tt > U741 > mark1
proper1 > U732 > U741 > ok1
proper1 > U732 > U741 > mark1
proper1 > U812 > ok1
proper1 > U812 > mark1
proper1 > U822 > U831 > tt > U122 > ok1
proper1 > U822 > U831 > tt > U122 > mark1
proper1 > U822 > U831 > tt > isNeList1 > U413 > U423 > ok1
proper1 > U822 > U831 > tt > isNeList1 > U413 > U423 > mark1
proper1 > U822 > U831 > tt > U223 > U233 > U243 > ok1
proper1 > U822 > U831 > tt > U223 > U233 > U243 > mark1
proper1 > U822 > U831 > tt > U261 > ok1
proper1 > U822 > U831 > tt > U261 > mark1
proper1 > U822 > U831 > tt > U322 > ok1
proper1 > U822 > U831 > tt > U322 > mark1
proper1 > U822 > U831 > tt > U452 > U461 > ok1
proper1 > U822 > U831 > tt > U452 > U461 > mark1
proper1 > U822 > U831 > tt > U543 > U552 > ok1
proper1 > U822 > U831 > tt > U543 > U552 > mark1
proper1 > U822 > U831 > tt > U622 > ok1
proper1 > U822 > U831 > tt > U622 > mark1
proper1 > U822 > U831 > tt > U722 > mark1
proper1 > U822 > U831 > tt > U722 > isPal1 > ok1
proper1 > U822 > U831 > tt > U741 > ok1
proper1 > U822 > U831 > tt > U741 > mark1
proper1 > a > ok1
proper1 > a > mark1
proper1 > i > ok1
proper1 > i > mark1
proper1 > o > ok1
proper1 > o > mark1
proper1 > u > ok1
proper1 > u > mark1

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

(109) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(110) PisEmptyProof (EQUIVALENT transformation)

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

(111) TRUE

(112) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(113) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U611(ok(X1), ok(X2)) → U611(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U611(x1, x2)  =  x2
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  x3
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  U24(x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
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)  =  x3
U55(x1, x2)  =  U55(x2)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  x2
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U513 > ok1
active1 > U241 > isList1 > tt > U131 > ok1
active1 > U241 > isList1 > tt > isNeList1 > U513 > ok1
active1 > U241 > isList1 > tt > U251 > U261 > ok1
active1 > U241 > isList1 > tt > U322 > ok1
active1 > U241 > isList1 > tt > U423 > ok1
active1 > U241 > isList1 > tt > U461 > ok1
active1 > U241 > isList1 > tt > U522 > ok1
active1 > U241 > isList1 > tt > U561 > ok1
active1 > U241 > isList1 > tt > U622 > ok1
active1 > U241 > isList1 > tt > U831 > ok1
active1 > U241 > isList1 > tt > isNePal1 > ok1
active1 > U311 > ok1
active1 > U331 > tt > U131 > ok1
active1 > U331 > tt > isNeList1 > U513 > ok1
active1 > U331 > tt > U251 > U261 > ok1
active1 > U331 > tt > U322 > ok1
active1 > U331 > tt > U423 > ok1
active1 > U331 > tt > U461 > ok1
active1 > U331 > tt > U522 > ok1
active1 > U331 > tt > U561 > ok1
active1 > U331 > tt > U622 > ok1
active1 > U331 > tt > U831 > ok1
active1 > U331 > tt > isNePal1 > ok1
active1 > U413 > U423 > ok1
active1 > U432 > U443 > isList1 > tt > U131 > ok1
active1 > U432 > U443 > isList1 > tt > isNeList1 > U513 > ok1
active1 > U432 > U443 > isList1 > tt > U251 > U261 > ok1
active1 > U432 > U443 > isList1 > tt > U322 > ok1
active1 > U432 > U443 > isList1 > tt > U423 > ok1
active1 > U432 > U443 > isList1 > tt > U461 > ok1
active1 > U432 > U443 > isList1 > tt > U522 > ok1
active1 > U432 > U443 > isList1 > tt > U561 > ok1
active1 > U432 > U443 > isList1 > tt > U622 > ok1
active1 > U432 > U443 > isList1 > tt > U831 > ok1
active1 > U432 > U443 > isList1 > tt > isNePal1 > ok1
active1 > U432 > U443 > U452 > isNeList1 > U513 > ok1
active1 > U432 > U443 > U452 > U461 > ok1
active1 > U533 > ok1
active1 > U551 > U561 > ok1
active1 > U612 > ok1
active1 > U713 > U722 > ok1
active1 > U732 > ok1
active1 > U741 > tt > U131 > ok1
active1 > U741 > tt > isNeList1 > U513 > ok1
active1 > U741 > tt > U251 > U261 > ok1
active1 > U741 > tt > U322 > ok1
active1 > U741 > tt > U423 > ok1
active1 > U741 > tt > U461 > ok1
active1 > U741 > tt > U522 > ok1
active1 > U741 > tt > U561 > ok1
active1 > U741 > tt > U622 > ok1
active1 > U741 > tt > U831 > ok1
active1 > U741 > tt > isNePal1 > ok1
active1 > U811 > ok1
active1 > U921 > tt > U131 > ok1
active1 > U921 > tt > isNeList1 > U513 > ok1
active1 > U921 > tt > U251 > U261 > ok1
active1 > U921 > tt > U322 > ok1
active1 > U921 > tt > U423 > ok1
active1 > U921 > tt > U461 > ok1
active1 > U921 > tt > U522 > ok1
active1 > U921 > tt > U561 > ok1
active1 > U921 > tt > U622 > ok1
active1 > U921 > tt > U831 > ok1
active1 > U921 > tt > isNePal1 > ok1
proper1 > _2 > U513 > ok1
proper1 > nil > tt > U131 > ok1
proper1 > nil > tt > isNeList1 > U513 > ok1
proper1 > nil > tt > U251 > U261 > ok1
proper1 > nil > tt > U322 > ok1
proper1 > nil > tt > U423 > ok1
proper1 > nil > tt > U461 > ok1
proper1 > nil > tt > U522 > ok1
proper1 > nil > tt > U561 > ok1
proper1 > nil > tt > U622 > ok1
proper1 > nil > tt > U831 > ok1
proper1 > nil > tt > isNePal1 > ok1
proper1 > U241 > isList1 > tt > U131 > ok1
proper1 > U241 > isList1 > tt > isNeList1 > U513 > ok1
proper1 > U241 > isList1 > tt > U251 > U261 > ok1
proper1 > U241 > isList1 > tt > U322 > ok1
proper1 > U241 > isList1 > tt > U423 > ok1
proper1 > U241 > isList1 > tt > U461 > ok1
proper1 > U241 > isList1 > tt > U522 > ok1
proper1 > U241 > isList1 > tt > U561 > ok1
proper1 > U241 > isList1 > tt > U622 > ok1
proper1 > U241 > isList1 > tt > U831 > ok1
proper1 > U241 > isList1 > tt > isNePal1 > ok1
proper1 > U311 > ok1
proper1 > U331 > tt > U131 > ok1
proper1 > U331 > tt > isNeList1 > U513 > ok1
proper1 > U331 > tt > U251 > U261 > ok1
proper1 > U331 > tt > U322 > ok1
proper1 > U331 > tt > U423 > ok1
proper1 > U331 > tt > U461 > ok1
proper1 > U331 > tt > U522 > ok1
proper1 > U331 > tt > U561 > ok1
proper1 > U331 > tt > U622 > ok1
proper1 > U331 > tt > U831 > ok1
proper1 > U331 > tt > isNePal1 > ok1
proper1 > U413 > U423 > ok1
proper1 > U432 > U443 > isList1 > tt > U131 > ok1
proper1 > U432 > U443 > isList1 > tt > isNeList1 > U513 > ok1
proper1 > U432 > U443 > isList1 > tt > U251 > U261 > ok1
proper1 > U432 > U443 > isList1 > tt > U322 > ok1
proper1 > U432 > U443 > isList1 > tt > U423 > ok1
proper1 > U432 > U443 > isList1 > tt > U461 > ok1
proper1 > U432 > U443 > isList1 > tt > U522 > ok1
proper1 > U432 > U443 > isList1 > tt > U561 > ok1
proper1 > U432 > U443 > isList1 > tt > U622 > ok1
proper1 > U432 > U443 > isList1 > tt > U831 > ok1
proper1 > U432 > U443 > isList1 > tt > isNePal1 > ok1
proper1 > U432 > U443 > U452 > isNeList1 > U513 > ok1
proper1 > U432 > U443 > U452 > U461 > ok1
proper1 > U533 > ok1
proper1 > U551 > U561 > ok1
proper1 > U612 > ok1
proper1 > U713 > U722 > ok1
proper1 > U732 > ok1
proper1 > U741 > tt > U131 > ok1
proper1 > U741 > tt > isNeList1 > U513 > ok1
proper1 > U741 > tt > U251 > U261 > ok1
proper1 > U741 > tt > U322 > ok1
proper1 > U741 > tt > U423 > ok1
proper1 > U741 > tt > U461 > ok1
proper1 > U741 > tt > U522 > ok1
proper1 > U741 > tt > U561 > ok1
proper1 > U741 > tt > U622 > ok1
proper1 > U741 > tt > U831 > ok1
proper1 > U741 > tt > isNePal1 > ok1
proper1 > U811 > ok1
proper1 > U921 > tt > U131 > ok1
proper1 > U921 > tt > isNeList1 > U513 > ok1
proper1 > U921 > tt > U251 > U261 > ok1
proper1 > U921 > tt > U322 > ok1
proper1 > U921 > tt > U423 > ok1
proper1 > U921 > tt > U461 > ok1
proper1 > U921 > tt > U522 > ok1
proper1 > U921 > tt > U561 > ok1
proper1 > U921 > tt > U622 > ok1
proper1 > U921 > tt > U831 > ok1
proper1 > U921 > tt > isNePal1 > ok1
proper1 > a > tt > U131 > ok1
proper1 > a > tt > isNeList1 > U513 > ok1
proper1 > a > tt > U251 > U261 > ok1
proper1 > a > tt > U322 > ok1
proper1 > a > tt > U423 > ok1
proper1 > a > tt > U461 > ok1
proper1 > a > tt > U522 > ok1
proper1 > a > tt > U561 > ok1
proper1 > a > tt > U622 > ok1
proper1 > a > tt > U831 > ok1
proper1 > a > tt > isNePal1 > ok1
proper1 > e > ok1
proper1 > i > ok1
proper1 > o > tt > U131 > ok1
proper1 > o > tt > isNeList1 > U513 > ok1
proper1 > o > tt > U251 > U261 > ok1
proper1 > o > tt > U322 > ok1
proper1 > o > tt > U423 > ok1
proper1 > o > tt > U461 > ok1
proper1 > o > tt > U522 > ok1
proper1 > o > tt > U561 > ok1
proper1 > o > tt > U622 > ok1
proper1 > o > tt > U831 > ok1
proper1 > o > tt > isNePal1 > ok1
proper1 > u > ok1
top > ok1

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

(114) Obligation:

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

U611(mark(X1), X2) → U611(X1, X2)

The TRS R consists of the following rules:

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

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

(115) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U611(mark(X1), X2) → U611(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U611(x1, x2)  =  U611(x1)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
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)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > isQid > ok
active1 > _2 > U411 > mark1
active1 > _2 > U411 > ok
active1 > U121 > mark1
active1 > U121 > ok
active1 > isPalListKind > tt > isQid > ok
active1 > isPalListKind > U911 > mark1
active1 > isPalListKind > U911 > ok
active1 > isNeList > mark1
active1 > isNeList > ok
active1 > U221 > mark1
active1 > U221 > ok
active1 > U231 > U241 > isList > mark1
active1 > U231 > U241 > isList > tt > isQid > ok
active1 > U261 > mark1
active1 > U261 > tt > isQid > ok
active1 > U321 > mark1
active1 > U321 > isQid > ok
active1 > U331 > mark1
active1 > U331 > tt > isQid > ok
active1 > U461 > mark1
active1 > U461 > tt > isQid > ok
active1 > U541 > mark1
active1 > U541 > ok
active1 > U631 > mark1
active1 > U631 > tt > isQid > ok
active1 > U713 > U722 > mark1
active1 > U713 > U722 > ok
active1 > isPal1 > tt > isQid > ok
active1 > isPal1 > U812 > mark1
active1 > isPal1 > U812 > ok
active1 > U822 > mark1
active1 > U822 > ok
active1 > U831 > mark1
active1 > U831 > tt > isQid > ok
proper1 > _2 > isQid > ok
proper1 > _2 > U411 > mark1
proper1 > _2 > U411 > ok
proper1 > nil > ok
proper1 > U121 > mark1
proper1 > U121 > ok
proper1 > isPalListKind > tt > isQid > ok
proper1 > isPalListKind > U911 > mark1
proper1 > isPalListKind > U911 > ok
proper1 > isNeList > mark1
proper1 > isNeList > ok
proper1 > U221 > mark1
proper1 > U221 > ok
proper1 > U231 > U241 > isList > mark1
proper1 > U231 > U241 > isList > tt > isQid > ok
proper1 > U261 > mark1
proper1 > U261 > tt > isQid > ok
proper1 > U321 > mark1
proper1 > U321 > isQid > ok
proper1 > U331 > mark1
proper1 > U331 > tt > isQid > ok
proper1 > U461 > mark1
proper1 > U461 > tt > isQid > ok
proper1 > U541 > mark1
proper1 > U541 > ok
proper1 > U631 > mark1
proper1 > U631 > tt > isQid > ok
proper1 > U713 > U722 > mark1
proper1 > U713 > U722 > ok
proper1 > isPal1 > tt > isQid > ok
proper1 > isPal1 > U812 > mark1
proper1 > isPal1 > U812 > ok
proper1 > U822 > mark1
proper1 > U822 > ok
proper1 > U831 > mark1
proper1 > U831 > tt > isQid > ok
proper1 > a
proper1 > e
proper1 > i > ok
proper1 > o > mark1
proper1 > o > tt > isQid > ok
proper1 > u > mark1
proper1 > u > tt > isQid > ok

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

(116) Obligation:

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

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

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

(117) PisEmptyProof (EQUIVALENT transformation)

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

(118) TRUE

(119) Obligation:

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

U561(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(120) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U561(mark(X)) → U561(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U561(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(121) Obligation:

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

U561(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(122) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U561(ok(X)) → U561(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U561(x1)  =  U561(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(123) Obligation:

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

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

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

(124) PisEmptyProof (EQUIVALENT transformation)

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

(125) TRUE

(126) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(127) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U551(mark(X1), X2) → U551(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U551(x1, x2)  =  U551(x1, x2)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  U52(x1)
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
a > mark1
e > tt > U251 > mark1
e > tt > U261 > mark1
e > tt > U431 > mark1
e > tt > U461 > mark1
e > tt > U722 > mark1
e > tt > U741 > mark1
e > tt > U822 > mark1
i > tt > U251 > mark1
i > tt > U261 > mark1
i > tt > U431 > mark1
i > tt > U461 > mark1
i > tt > U722 > mark1
i > tt > U741 > mark1
i > tt > U822 > mark1
top > active1 > _2 > isQid > mark1
top > active1 > _2 > U713 > mark1
top > active1 > U131 > tt > U251 > mark1
top > active1 > U131 > tt > U261 > mark1
top > active1 > U131 > tt > U431 > mark1
top > active1 > U131 > tt > U461 > mark1
top > active1 > U131 > tt > U722 > mark1
top > active1 > U131 > tt > U741 > mark1
top > active1 > U131 > tt > U822 > mark1
top > active1 > isNeList > U311 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U251 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U261 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U431 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U461 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U722 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U741 > mark1
top > active1 > U211 > U221 > U231 > isPalListKind > tt > U822 > mark1
top > active1 > U411 > mark1
top > active1 > U421 > isPalListKind > tt > U251 > mark1
top > active1 > U421 > isPalListKind > tt > U261 > mark1
top > active1 > U421 > isPalListKind > tt > U431 > mark1
top > active1 > U421 > isPalListKind > tt > U461 > mark1
top > active1 > U421 > isPalListKind > tt > U722 > mark1
top > active1 > U421 > isPalListKind > tt > U741 > mark1
top > active1 > U421 > isPalListKind > tt > U822 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U251 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U261 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U431 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U461 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U722 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U741 > mark1
top > active1 > U441 > isList > isPalListKind > tt > U822 > mark1
top > active1 > U511 > isPalListKind > tt > U251 > mark1
top > active1 > U511 > isPalListKind > tt > U261 > mark1
top > active1 > U511 > isPalListKind > tt > U431 > mark1
top > active1 > U511 > isPalListKind > tt > U461 > mark1
top > active1 > U511 > isPalListKind > tt > U722 > mark1
top > active1 > U511 > isPalListKind > tt > U741 > mark1
top > active1 > U511 > isPalListKind > tt > U822 > mark1
top > active1 > U511 > U521 > mark1
top > active1 > U531 > isPalListKind > tt > U251 > mark1
top > active1 > U531 > isPalListKind > tt > U261 > mark1
top > active1 > U531 > isPalListKind > tt > U431 > mark1
top > active1 > U531 > isPalListKind > tt > U461 > mark1
top > active1 > U531 > isPalListKind > tt > U722 > mark1
top > active1 > U531 > isPalListKind > tt > U741 > mark1
top > active1 > U531 > isPalListKind > tt > U822 > mark1
top > active1 > U812 > U822 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U251 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U261 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U431 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U461 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U722 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U741 > mark1
top > active1 > isNePal1 > isPalListKind > tt > U822 > mark1
top > active1 > isNePal1 > isQid > mark1
top > active1 > isNePal1 > U612 > mark1
top > active1 > isNePal1 > U713 > mark1
top > active1 > U911 > isPalListKind > tt > U251 > mark1
top > active1 > U911 > isPalListKind > tt > U261 > mark1
top > active1 > U911 > isPalListKind > tt > U431 > mark1
top > active1 > U911 > isPalListKind > tt > U461 > mark1
top > active1 > U911 > isPalListKind > tt > U722 > mark1
top > active1 > U911 > isPalListKind > tt > U741 > mark1
top > active1 > U911 > isPalListKind > tt > U822 > mark1
top > active1 > U911 > U921 > tt > U251 > mark1
top > active1 > U911 > U921 > tt > U261 > mark1
top > active1 > U911 > U921 > tt > U431 > mark1
top > active1 > U911 > U921 > tt > U461 > mark1
top > active1 > U911 > U921 > tt > U722 > mark1
top > active1 > U911 > U921 > tt > U741 > mark1
top > active1 > U911 > U921 > tt > U822 > mark1

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

(128) Obligation:

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

U551(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(129) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U551(ok(X1), ok(X2)) → U551(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U551(x1, x2)  =  x2
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x2, x3)
U23(x1, x2, x3)  =  U23(x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  x2
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U213 > ok1
active1 > _2 > U413 > ok1
active1 > _2 > U512 > ok1
active1 > _2 > U912 > ok1
active1 > isNeList1 > U512 > ok1
active1 > U222 > U232 > ok1
active1 > U243 > ok1
active1 > U252 > ok1
active1 > U312 > ok1
active1 > U423 > isPalListKind1 > tt
active1 > U423 > isPalListKind1 > U912 > ok1
active1 > U423 > U433 > U443 > U452 > ok1
active1 > U461 > ok1
active1 > U461 > tt
active1 > U523 > ok1
active1 > U612 > U621 > ok1
active1 > U631 > ok1
active1 > U631 > tt
active1 > U713 > isPalListKind1 > tt
active1 > U713 > isPalListKind1 > U912 > ok1
active1 > U713 > U721 > ok1
active1 > U812 > ok1
active1 > U831 > ok1
active1 > U831 > tt
active1 > isNePal1 > ok1
proper1 > _2 > U213 > ok1
proper1 > _2 > U413 > ok1
proper1 > _2 > U512 > ok1
proper1 > _2 > U912 > ok1
proper1 > nil
proper1 > isNeList1 > U512 > ok1
proper1 > U222 > U232 > ok1
proper1 > U243 > ok1
proper1 > U252 > ok1
proper1 > U312 > ok1
proper1 > U423 > isPalListKind1 > tt
proper1 > U423 > isPalListKind1 > U912 > ok1
proper1 > U423 > U433 > U443 > U452 > ok1
proper1 > U461 > ok1
proper1 > U461 > tt
proper1 > U523 > ok1
proper1 > U612 > U621 > ok1
proper1 > U631 > ok1
proper1 > U631 > tt
proper1 > U713 > isPalListKind1 > tt
proper1 > U713 > isPalListKind1 > U912 > ok1
proper1 > U713 > U721 > ok1
proper1 > U812 > ok1
proper1 > U831 > ok1
proper1 > U831 > tt
proper1 > isNePal1 > ok1
proper1 > a > ok1
proper1 > a > tt
proper1 > e
proper1 > i > ok1
proper1 > i > tt
proper1 > o
proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(130) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(131) PisEmptyProof (EQUIVALENT transformation)

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

(132) TRUE

(133) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(134) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(ok(X1), ok(X2), ok(X3)) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  U541(x1, x2, x3)
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x2)
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
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(x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, 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)  =  x2
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
i > tt > U223 > ok1 > U54^13
i > tt > U252 > ok1 > U54^13
i > tt > U322 > ok1 > U54^13
i > tt > U422 > ok1 > U54^13
i > tt > U442 > ok1 > U54^13
i > tt > U542 > isNeList1 > ok1 > U54^13
i > tt > U721 > ok1 > U54^13
i > tt > U831 > ok1 > U54^13
top > active1 > _2 > ok1 > U54^13
top > active1 > U111 > ok1 > U54^13
top > active1 > U131 > tt > U223 > ok1 > U54^13
top > active1 > U131 > tt > U252 > ok1 > U54^13
top > active1 > U131 > tt > U322 > ok1 > U54^13
top > active1 > U131 > tt > U422 > ok1 > U54^13
top > active1 > U131 > tt > U442 > ok1 > U54^13
top > active1 > U131 > tt > U542 > isNeList1 > ok1 > U54^13
top > active1 > U131 > tt > U721 > ok1 > U54^13
top > active1 > U131 > tt > U831 > ok1 > U54^13
top > active1 > U213 > U223 > ok1 > U54^13
top > active1 > U233 > ok1 > U54^13
top > active1 > U242 > U252 > ok1 > U54^13
top > active1 > isList1 > tt > U223 > ok1 > U54^13
top > active1 > isList1 > tt > U252 > ok1 > U54^13
top > active1 > isList1 > tt > U322 > ok1 > U54^13
top > active1 > isList1 > tt > U422 > ok1 > U54^13
top > active1 > isList1 > tt > U442 > ok1 > U54^13
top > active1 > isList1 > tt > U542 > isNeList1 > ok1 > U54^13
top > active1 > isList1 > tt > U721 > ok1 > U54^13
top > active1 > isList1 > tt > U831 > ok1 > U54^13
top > active1 > U311 > U322 > ok1 > U54^13
top > active1 > U413 > U422 > ok1 > U54^13
top > active1 > U432 > U442 > ok1 > U54^13
top > active1 > U512 > ok1 > U54^13
top > active1 > U523 > ok1 > U54^13
top > active1 > U631 > tt > U223 > ok1 > U54^13
top > active1 > U631 > tt > U252 > ok1 > U54^13
top > active1 > U631 > tt > U322 > ok1 > U54^13
top > active1 > U631 > tt > U422 > ok1 > U54^13
top > active1 > U631 > tt > U442 > ok1 > U54^13
top > active1 > U631 > tt > U542 > isNeList1 > ok1 > U54^13
top > active1 > U631 > tt > U721 > ok1 > U54^13
top > active1 > U631 > tt > U831 > ok1 > U54^13
top > active1 > U731 > ok1 > U54^13
top > active1 > U741 > tt > U223 > ok1 > U54^13
top > active1 > U741 > tt > U252 > ok1 > U54^13
top > active1 > U741 > tt > U322 > ok1 > U54^13
top > active1 > U741 > tt > U422 > ok1 > U54^13
top > active1 > U741 > tt > U442 > ok1 > U54^13
top > active1 > U741 > tt > U542 > isNeList1 > ok1 > U54^13
top > active1 > U741 > tt > U721 > ok1 > U54^13
top > active1 > U741 > tt > U831 > ok1 > U54^13
top > proper1 > _2 > ok1 > U54^13
top > proper1 > nil > U54^13
top > proper1 > U111 > ok1 > U54^13
top > proper1 > U131 > tt > U223 > ok1 > U54^13
top > proper1 > U131 > tt > U252 > ok1 > U54^13
top > proper1 > U131 > tt > U322 > ok1 > U54^13
top > proper1 > U131 > tt > U422 > ok1 > U54^13
top > proper1 > U131 > tt > U442 > ok1 > U54^13
top > proper1 > U131 > tt > U542 > isNeList1 > ok1 > U54^13
top > proper1 > U131 > tt > U721 > ok1 > U54^13
top > proper1 > U131 > tt > U831 > ok1 > U54^13
top > proper1 > U213 > U223 > ok1 > U54^13
top > proper1 > U233 > ok1 > U54^13
top > proper1 > U242 > U252 > ok1 > U54^13
top > proper1 > isList1 > tt > U223 > ok1 > U54^13
top > proper1 > isList1 > tt > U252 > ok1 > U54^13
top > proper1 > isList1 > tt > U322 > ok1 > U54^13
top > proper1 > isList1 > tt > U422 > ok1 > U54^13
top > proper1 > isList1 > tt > U442 > ok1 > U54^13
top > proper1 > isList1 > tt > U542 > isNeList1 > ok1 > U54^13
top > proper1 > isList1 > tt > U721 > ok1 > U54^13
top > proper1 > isList1 > tt > U831 > ok1 > U54^13
top > proper1 > U311 > U322 > ok1 > U54^13
top > proper1 > U413 > U422 > ok1 > U54^13
top > proper1 > U432 > U442 > ok1 > U54^13
top > proper1 > U512 > ok1 > U54^13
top > proper1 > U523 > ok1 > U54^13
top > proper1 > U631 > tt > U223 > ok1 > U54^13
top > proper1 > U631 > tt > U252 > ok1 > U54^13
top > proper1 > U631 > tt > U322 > ok1 > U54^13
top > proper1 > U631 > tt > U422 > ok1 > U54^13
top > proper1 > U631 > tt > U442 > ok1 > U54^13
top > proper1 > U631 > tt > U542 > isNeList1 > ok1 > U54^13
top > proper1 > U631 > tt > U721 > ok1 > U54^13
top > proper1 > U631 > tt > U831 > ok1 > U54^13
top > proper1 > U731 > ok1 > U54^13
top > proper1 > isPal1 > tt > U223 > ok1 > U54^13
top > proper1 > isPal1 > tt > U252 > ok1 > U54^13
top > proper1 > isPal1 > tt > U322 > ok1 > U54^13
top > proper1 > isPal1 > tt > U422 > ok1 > U54^13
top > proper1 > isPal1 > tt > U442 > ok1 > U54^13
top > proper1 > isPal1 > tt > U542 > isNeList1 > ok1 > U54^13
top > proper1 > isPal1 > tt > U721 > ok1 > U54^13
top > proper1 > isPal1 > tt > U831 > ok1 > U54^13
top > proper1 > U741 > tt > U223 > ok1 > U54^13
top > proper1 > U741 > tt > U252 > ok1 > U54^13
top > proper1 > U741 > tt > U322 > ok1 > U54^13
top > proper1 > U741 > tt > U422 > ok1 > U54^13
top > proper1 > U741 > tt > U442 > ok1 > U54^13
top > proper1 > U741 > tt > U542 > isNeList1 > ok1 > U54^13
top > proper1 > U741 > tt > U721 > ok1 > U54^13
top > proper1 > U741 > tt > U831 > ok1 > U54^13
top > proper1 > a > ok1 > U54^13
top > proper1 > e > ok1 > U54^13
top > proper1 > o > ok1 > U54^13
top > proper1 > u > ok1 > U54^13

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

(135) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(136) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U541(mark(X1), X2, X3) → U541(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U541(x1, x2, x3)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1 > ok
active1 > _2 > isQid > tt > ok
active1 > U111 > U121 > mark1 > ok
active1 > U111 > isPalListKind > mark1 > ok
active1 > U111 > isPalListKind > tt > ok
active1 > U131 > mark1 > ok
active1 > U131 > tt > ok
active1 > U231 > U241 > mark1 > ok
active1 > U231 > U241 > isList > tt > ok
active1 > U251 > mark1 > ok
active1 > U251 > isList > tt > ok
active1 > U261 > mark1 > ok
active1 > U261 > tt > ok
active1 > U451 > isNeList > U311 > mark1 > ok
active1 > U531 > mark1 > ok
active1 > U711 > isPalListKind > mark1 > ok
active1 > U711 > isPalListKind > tt > ok
active1 > U731 > U741 > mark1 > ok
active1 > U731 > U741 > tt > ok
active1 > isPal > tt > ok
active1 > U831 > mark1 > ok
active1 > U831 > tt > ok
active1 > isNePal > isPalListKind > mark1 > ok
active1 > isNePal > isPalListKind > tt > ok
active1 > isNePal > isQid > tt > ok
active1 > U911 > mark1 > ok
nil > ok
a > ok
e > ok
i > ok
o > ok
u > tt > ok
top > ok

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

(137) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(138) PisEmptyProof (EQUIVALENT transformation)

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

(139) TRUE

(140) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(141) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(ok(X1), ok(X2), ok(X3)) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  U531(x2)
ok(x1)  =  ok(x1)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U713 > ok1
active1 > _2 > U713 > mark1
active1 > _2 > U912 > U921 > ok1
active1 > _2 > U912 > U921 > mark1
active1 > U112 > ok1
active1 > U112 > mark1
active1 > U122 > U131 > ok1
active1 > U122 > U131 > mark1
active1 > isPalListKind1 > U912 > U921 > ok1
active1 > isPalListKind1 > U912 > U921 > mark1
active1 > isNeList1 > U312 > ok1
active1 > isNeList1 > U312 > mark1
active1 > isNeList1 > U413 > U423 > ok1
active1 > isNeList1 > U413 > U423 > mark1
active1 > isNeList1 > U513 > U523 > ok1
active1 > isNeList1 > U513 > U523 > mark1
active1 > U213 > U223 > ok1
active1 > U213 > U223 > mark1
active1 > U233 > U243 > U252 > ok1
active1 > U233 > U243 > U252 > mark1
active1 > U322 > ok1
active1 > U322 > mark1
active1 > U331 > ok1
active1 > U331 > mark1
active1 > U433 > U443 > ok1
active1 > U433 > U443 > mark1
active1 > U452 > ok1
active1 > U452 > mark1
active1 > U461 > ok1
active1 > U461 > mark1
active1 > U533 > ok1
active1 > U533 > mark1
active1 > U543 > U552 > U561 > ok1
active1 > U543 > U552 > U561 > mark1
active1 > U612 > U622 > ok1
active1 > U612 > U622 > mark1
active1 > U631 > ok1
active1 > U631 > mark1
active1 > U722 > ok1
active1 > U722 > mark1
active1 > U732 > U741 > ok1
active1 > U732 > U741 > mark1
active1 > U812 > U822 > ok1
active1 > U812 > U822 > mark1
active1 > U831 > ok1
active1 > U831 > mark1
nil > tt > U122 > U131 > ok1
nil > tt > U122 > U131 > mark1
nil > tt > isPalListKind1 > U912 > U921 > ok1
nil > tt > isPalListKind1 > U912 > U921 > mark1
nil > tt > isNeList1 > U312 > ok1
nil > tt > isNeList1 > U312 > mark1
nil > tt > isNeList1 > U413 > U423 > ok1
nil > tt > isNeList1 > U413 > U423 > mark1
nil > tt > isNeList1 > U513 > U523 > ok1
nil > tt > isNeList1 > U513 > U523 > mark1
nil > tt > U223 > ok1
nil > tt > U223 > mark1
nil > tt > U233 > U243 > U252 > ok1
nil > tt > U233 > U243 > U252 > mark1
nil > tt > U322 > ok1
nil > tt > U322 > mark1
nil > tt > U331 > ok1
nil > tt > U331 > mark1
nil > tt > U433 > U443 > ok1
nil > tt > U433 > U443 > mark1
nil > tt > U452 > ok1
nil > tt > U452 > mark1
nil > tt > U461 > ok1
nil > tt > U461 > mark1
nil > tt > U533 > ok1
nil > tt > U533 > mark1
nil > tt > U543 > U552 > U561 > ok1
nil > tt > U543 > U552 > U561 > mark1
nil > tt > U622 > ok1
nil > tt > U622 > mark1
nil > tt > U631 > ok1
nil > tt > U631 > mark1
nil > tt > U722 > ok1
nil > tt > U722 > mark1
nil > tt > U732 > U741 > ok1
nil > tt > U732 > U741 > mark1
nil > tt > U822 > ok1
nil > tt > U822 > mark1
nil > tt > U831 > ok1
nil > tt > U831 > mark1
proper1 > _2 > U713 > ok1
proper1 > _2 > U713 > mark1
proper1 > _2 > U912 > U921 > ok1
proper1 > _2 > U912 > U921 > mark1
proper1 > U112 > ok1
proper1 > U112 > mark1
proper1 > U213 > U223 > ok1
proper1 > U213 > U223 > mark1
proper1 > U612 > U622 > ok1
proper1 > U612 > U622 > mark1
proper1 > U812 > U822 > ok1
proper1 > U812 > U822 > mark1
proper1 > a > tt > U122 > U131 > ok1
proper1 > a > tt > U122 > U131 > mark1
proper1 > a > tt > isPalListKind1 > U912 > U921 > ok1
proper1 > a > tt > isPalListKind1 > U912 > U921 > mark1
proper1 > a > tt > isNeList1 > U312 > ok1
proper1 > a > tt > isNeList1 > U312 > mark1
proper1 > a > tt > isNeList1 > U413 > U423 > ok1
proper1 > a > tt > isNeList1 > U413 > U423 > mark1
proper1 > a > tt > isNeList1 > U513 > U523 > ok1
proper1 > a > tt > isNeList1 > U513 > U523 > mark1
proper1 > a > tt > U223 > ok1
proper1 > a > tt > U223 > mark1
proper1 > a > tt > U233 > U243 > U252 > ok1
proper1 > a > tt > U233 > U243 > U252 > mark1
proper1 > a > tt > U322 > ok1
proper1 > a > tt > U322 > mark1
proper1 > a > tt > U331 > ok1
proper1 > a > tt > U331 > mark1
proper1 > a > tt > U433 > U443 > ok1
proper1 > a > tt > U433 > U443 > mark1
proper1 > a > tt > U452 > ok1
proper1 > a > tt > U452 > mark1
proper1 > a > tt > U461 > ok1
proper1 > a > tt > U461 > mark1
proper1 > a > tt > U533 > ok1
proper1 > a > tt > U533 > mark1
proper1 > a > tt > U543 > U552 > U561 > ok1
proper1 > a > tt > U543 > U552 > U561 > mark1
proper1 > a > tt > U622 > ok1
proper1 > a > tt > U622 > mark1
proper1 > a > tt > U631 > ok1
proper1 > a > tt > U631 > mark1
proper1 > a > tt > U722 > ok1
proper1 > a > tt > U722 > mark1
proper1 > a > tt > U732 > U741 > ok1
proper1 > a > tt > U732 > U741 > mark1
proper1 > a > tt > U822 > ok1
proper1 > a > tt > U822 > mark1
proper1 > a > tt > U831 > ok1
proper1 > a > tt > U831 > mark1
proper1 > e > tt > U122 > U131 > ok1
proper1 > e > tt > U122 > U131 > mark1
proper1 > e > tt > isPalListKind1 > U912 > U921 > ok1
proper1 > e > tt > isPalListKind1 > U912 > U921 > mark1
proper1 > e > tt > isNeList1 > U312 > ok1
proper1 > e > tt > isNeList1 > U312 > mark1
proper1 > e > tt > isNeList1 > U413 > U423 > ok1
proper1 > e > tt > isNeList1 > U413 > U423 > mark1
proper1 > e > tt > isNeList1 > U513 > U523 > ok1
proper1 > e > tt > isNeList1 > U513 > U523 > mark1
proper1 > e > tt > U223 > ok1
proper1 > e > tt > U223 > mark1
proper1 > e > tt > U233 > U243 > U252 > ok1
proper1 > e > tt > U233 > U243 > U252 > mark1
proper1 > e > tt > U322 > ok1
proper1 > e > tt > U322 > mark1
proper1 > e > tt > U331 > ok1
proper1 > e > tt > U331 > mark1
proper1 > e > tt > U433 > U443 > ok1
proper1 > e > tt > U433 > U443 > mark1
proper1 > e > tt > U452 > ok1
proper1 > e > tt > U452 > mark1
proper1 > e > tt > U461 > ok1
proper1 > e > tt > U461 > mark1
proper1 > e > tt > U533 > ok1
proper1 > e > tt > U533 > mark1
proper1 > e > tt > U543 > U552 > U561 > ok1
proper1 > e > tt > U543 > U552 > U561 > mark1
proper1 > e > tt > U622 > ok1
proper1 > e > tt > U622 > mark1
proper1 > e > tt > U631 > ok1
proper1 > e > tt > U631 > mark1
proper1 > e > tt > U722 > ok1
proper1 > e > tt > U722 > mark1
proper1 > e > tt > U732 > U741 > ok1
proper1 > e > tt > U732 > U741 > mark1
proper1 > e > tt > U822 > ok1
proper1 > e > tt > U822 > mark1
proper1 > e > tt > U831 > ok1
proper1 > e > tt > U831 > mark1
proper1 > i > tt > U122 > U131 > ok1
proper1 > i > tt > U122 > U131 > mark1
proper1 > i > tt > isPalListKind1 > U912 > U921 > ok1
proper1 > i > tt > isPalListKind1 > U912 > U921 > mark1
proper1 > i > tt > isNeList1 > U312 > ok1
proper1 > i > tt > isNeList1 > U312 > mark1
proper1 > i > tt > isNeList1 > U413 > U423 > ok1
proper1 > i > tt > isNeList1 > U413 > U423 > mark1
proper1 > i > tt > isNeList1 > U513 > U523 > ok1
proper1 > i > tt > isNeList1 > U513 > U523 > mark1
proper1 > i > tt > U223 > ok1
proper1 > i > tt > U223 > mark1
proper1 > i > tt > U233 > U243 > U252 > ok1
proper1 > i > tt > U233 > U243 > U252 > mark1
proper1 > i > tt > U322 > ok1
proper1 > i > tt > U322 > mark1
proper1 > i > tt > U331 > ok1
proper1 > i > tt > U331 > mark1
proper1 > i > tt > U433 > U443 > ok1
proper1 > i > tt > U433 > U443 > mark1
proper1 > i > tt > U452 > ok1
proper1 > i > tt > U452 > mark1
proper1 > i > tt > U461 > ok1
proper1 > i > tt > U461 > mark1
proper1 > i > tt > U533 > ok1
proper1 > i > tt > U533 > mark1
proper1 > i > tt > U543 > U552 > U561 > ok1
proper1 > i > tt > U543 > U552 > U561 > mark1
proper1 > i > tt > U622 > ok1
proper1 > i > tt > U622 > mark1
proper1 > i > tt > U631 > ok1
proper1 > i > tt > U631 > mark1
proper1 > i > tt > U722 > ok1
proper1 > i > tt > U722 > mark1
proper1 > i > tt > U732 > U741 > ok1
proper1 > i > tt > U732 > U741 > mark1
proper1 > i > tt > U822 > ok1
proper1 > i > tt > U822 > mark1
proper1 > i > tt > U831 > ok1
proper1 > i > tt > U831 > mark1
proper1 > o > tt > U122 > U131 > ok1
proper1 > o > tt > U122 > U131 > mark1
proper1 > o > tt > isPalListKind1 > U912 > U921 > ok1
proper1 > o > tt > isPalListKind1 > U912 > U921 > mark1
proper1 > o > tt > isNeList1 > U312 > ok1
proper1 > o > tt > isNeList1 > U312 > mark1
proper1 > o > tt > isNeList1 > U413 > U423 > ok1
proper1 > o > tt > isNeList1 > U413 > U423 > mark1
proper1 > o > tt > isNeList1 > U513 > U523 > ok1
proper1 > o > tt > isNeList1 > U513 > U523 > mark1
proper1 > o > tt > U223 > ok1
proper1 > o > tt > U223 > mark1
proper1 > o > tt > U233 > U243 > U252 > ok1
proper1 > o > tt > U233 > U243 > U252 > mark1
proper1 > o > tt > U322 > ok1
proper1 > o > tt > U322 > mark1
proper1 > o > tt > U331 > ok1
proper1 > o > tt > U331 > mark1
proper1 > o > tt > U433 > U443 > ok1
proper1 > o > tt > U433 > U443 > mark1
proper1 > o > tt > U452 > ok1
proper1 > o > tt > U452 > mark1
proper1 > o > tt > U461 > ok1
proper1 > o > tt > U461 > mark1
proper1 > o > tt > U533 > ok1
proper1 > o > tt > U533 > mark1
proper1 > o > tt > U543 > U552 > U561 > ok1
proper1 > o > tt > U543 > U552 > U561 > mark1
proper1 > o > tt > U622 > ok1
proper1 > o > tt > U622 > mark1
proper1 > o > tt > U631 > ok1
proper1 > o > tt > U631 > mark1
proper1 > o > tt > U722 > ok1
proper1 > o > tt > U722 > mark1
proper1 > o > tt > U732 > U741 > ok1
proper1 > o > tt > U732 > U741 > mark1
proper1 > o > tt > U822 > ok1
proper1 > o > tt > U822 > mark1
proper1 > o > tt > U831 > ok1
proper1 > o > tt > U831 > mark1
proper1 > u > tt > U122 > U131 > ok1
proper1 > u > tt > U122 > U131 > mark1
proper1 > u > tt > isPalListKind1 > U912 > U921 > ok1
proper1 > u > tt > isPalListKind1 > U912 > U921 > mark1
proper1 > u > tt > isNeList1 > U312 > ok1
proper1 > u > tt > isNeList1 > U312 > mark1
proper1 > u > tt > isNeList1 > U413 > U423 > ok1
proper1 > u > tt > isNeList1 > U413 > U423 > mark1
proper1 > u > tt > isNeList1 > U513 > U523 > ok1
proper1 > u > tt > isNeList1 > U513 > U523 > mark1
proper1 > u > tt > U223 > ok1
proper1 > u > tt > U223 > mark1
proper1 > u > tt > U233 > U243 > U252 > ok1
proper1 > u > tt > U233 > U243 > U252 > mark1
proper1 > u > tt > U322 > ok1
proper1 > u > tt > U322 > mark1
proper1 > u > tt > U331 > ok1
proper1 > u > tt > U331 > mark1
proper1 > u > tt > U433 > U443 > ok1
proper1 > u > tt > U433 > U443 > mark1
proper1 > u > tt > U452 > ok1
proper1 > u > tt > U452 > mark1
proper1 > u > tt > U461 > ok1
proper1 > u > tt > U461 > mark1
proper1 > u > tt > U533 > ok1
proper1 > u > tt > U533 > mark1
proper1 > u > tt > U543 > U552 > U561 > ok1
proper1 > u > tt > U543 > U552 > U561 > mark1
proper1 > u > tt > U622 > ok1
proper1 > u > tt > U622 > mark1
proper1 > u > tt > U631 > ok1
proper1 > u > tt > U631 > mark1
proper1 > u > tt > U722 > ok1
proper1 > u > tt > U722 > mark1
proper1 > u > tt > U732 > U741 > ok1
proper1 > u > tt > U732 > U741 > mark1
proper1 > u > tt > U822 > ok1
proper1 > u > tt > U822 > mark1
proper1 > u > tt > U831 > ok1
proper1 > u > tt > U831 > mark1

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

(142) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(143) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U531(mark(X1), X2, X3) → U531(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U531(x1, x2, x3)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
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)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U213 > U223 > U233 > mark1
active1 > _2 > U213 > U223 > U233 > ok
active1 > _2 > isQid > tt
active1 > _2 > isQid > ok
active1 > _2 > U513 > U523 > mark1
active1 > _2 > U513 > U523 > ok
active1 > _2 > U713 > U722 > mark1
active1 > _2 > U713 > U722 > ok
active1 > _2 > U912 > U921 > mark1
active1 > _2 > U912 > U921 > tt
active1 > _2 > U912 > U921 > ok
active1 > U112 > mark1
active1 > U112 > ok
active1 > U122 > mark1
active1 > U122 > isNeList1 > ok
active1 > U131 > mark1
active1 > U131 > tt
active1 > U131 > ok
active1 > U243 > U252 > mark1
active1 > U243 > U252 > ok
active1 > U261 > mark1
active1 > U261 > tt
active1 > U261 > ok
active1 > U312 > mark1
active1 > U312 > ok
active1 > U413 > U423 > U433 > mark1
active1 > U413 > U423 > U433 > ok
active1 > U443 > U452 > mark1
active1 > U443 > U452 > isNeList1 > ok
active1 > U461 > mark1
active1 > U461 > tt
active1 > U461 > ok
active1 > U533 > U543 > isNeList1 > ok
active1 > U533 > U543 > U552 > mark1
active1 > U533 > U543 > U552 > ok
active1 > U561 > mark1
active1 > U561 > tt
active1 > U561 > ok
active1 > U631 > mark1
active1 > U631 > tt
active1 > U631 > ok
active1 > U732 > mark1
active1 > U732 > ok
active1 > U812 > mark1
active1 > U812 > ok
active1 > U822 > mark1
active1 > U822 > ok
active1 > isNePal1 > isQid > tt
active1 > isNePal1 > isQid > ok
active1 > isNePal1 > U612 > mark1
active1 > isNePal1 > U612 > ok
active1 > isNePal1 > U713 > U722 > mark1
active1 > isNePal1 > U713 > U722 > ok
proper1 > _2 > U213 > U223 > U233 > mark1
proper1 > _2 > U213 > U223 > U233 > ok
proper1 > _2 > isQid > tt
proper1 > _2 > isQid > ok
proper1 > _2 > U513 > U523 > mark1
proper1 > _2 > U513 > U523 > ok
proper1 > _2 > U713 > U722 > mark1
proper1 > _2 > U713 > U722 > ok
proper1 > _2 > U912 > U921 > mark1
proper1 > _2 > U912 > U921 > tt
proper1 > _2 > U912 > U921 > ok
proper1 > nil
proper1 > U112 > mark1
proper1 > U112 > ok
proper1 > U122 > mark1
proper1 > U122 > isNeList1 > ok
proper1 > U131 > mark1
proper1 > U131 > tt
proper1 > U131 > ok
proper1 > U243 > U252 > mark1
proper1 > U243 > U252 > ok
proper1 > U261 > mark1
proper1 > U261 > tt
proper1 > U261 > ok
proper1 > U312 > mark1
proper1 > U312 > ok
proper1 > U413 > U423 > U433 > mark1
proper1 > U413 > U423 > U433 > ok
proper1 > U443 > U452 > mark1
proper1 > U443 > U452 > isNeList1 > ok
proper1 > U461 > mark1
proper1 > U461 > tt
proper1 > U461 > ok
proper1 > U533 > U543 > isNeList1 > ok
proper1 > U533 > U543 > U552 > mark1
proper1 > U533 > U543 > U552 > ok
proper1 > U561 > mark1
proper1 > U561 > tt
proper1 > U561 > ok
proper1 > U631 > mark1
proper1 > U631 > tt
proper1 > U631 > ok
proper1 > U732 > mark1
proper1 > U732 > ok
proper1 > U812 > mark1
proper1 > U812 > ok
proper1 > U822 > mark1
proper1 > U822 > ok
proper1 > isNePal1 > isQid > tt
proper1 > isNePal1 > isQid > ok
proper1 > isNePal1 > U612 > mark1
proper1 > isNePal1 > U612 > ok
proper1 > isNePal1 > U713 > U722 > mark1
proper1 > isNePal1 > U713 > U722 > ok
proper1 > a
proper1 > e
proper1 > i > mark1
proper1 > i > tt
proper1 > i > ok
proper1 > o
proper1 > u > mark1
proper1 > u > tt
proper1 > u > ok

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

(144) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(145) PisEmptyProof (EQUIVALENT transformation)

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

(146) TRUE

(147) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(148) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(ok(X1), ok(X2), ok(X3)) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  U521(x1, x2, x3)
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x2)
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
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(x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, 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)  =  x2
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
i > tt > U223 > ok1 > U52^13
i > tt > U252 > ok1 > U52^13
i > tt > U322 > ok1 > U52^13
i > tt > U422 > ok1 > U52^13
i > tt > U442 > ok1 > U52^13
i > tt > U542 > isNeList1 > ok1 > U52^13
i > tt > U721 > ok1 > U52^13
i > tt > U831 > ok1 > U52^13
top > active1 > _2 > ok1 > U52^13
top > active1 > U111 > ok1 > U52^13
top > active1 > U131 > tt > U223 > ok1 > U52^13
top > active1 > U131 > tt > U252 > ok1 > U52^13
top > active1 > U131 > tt > U322 > ok1 > U52^13
top > active1 > U131 > tt > U422 > ok1 > U52^13
top > active1 > U131 > tt > U442 > ok1 > U52^13
top > active1 > U131 > tt > U542 > isNeList1 > ok1 > U52^13
top > active1 > U131 > tt > U721 > ok1 > U52^13
top > active1 > U131 > tt > U831 > ok1 > U52^13
top > active1 > U213 > U223 > ok1 > U52^13
top > active1 > U233 > ok1 > U52^13
top > active1 > U242 > U252 > ok1 > U52^13
top > active1 > isList1 > tt > U223 > ok1 > U52^13
top > active1 > isList1 > tt > U252 > ok1 > U52^13
top > active1 > isList1 > tt > U322 > ok1 > U52^13
top > active1 > isList1 > tt > U422 > ok1 > U52^13
top > active1 > isList1 > tt > U442 > ok1 > U52^13
top > active1 > isList1 > tt > U542 > isNeList1 > ok1 > U52^13
top > active1 > isList1 > tt > U721 > ok1 > U52^13
top > active1 > isList1 > tt > U831 > ok1 > U52^13
top > active1 > U311 > U322 > ok1 > U52^13
top > active1 > U413 > U422 > ok1 > U52^13
top > active1 > U432 > U442 > ok1 > U52^13
top > active1 > U512 > ok1 > U52^13
top > active1 > U523 > ok1 > U52^13
top > active1 > U631 > tt > U223 > ok1 > U52^13
top > active1 > U631 > tt > U252 > ok1 > U52^13
top > active1 > U631 > tt > U322 > ok1 > U52^13
top > active1 > U631 > tt > U422 > ok1 > U52^13
top > active1 > U631 > tt > U442 > ok1 > U52^13
top > active1 > U631 > tt > U542 > isNeList1 > ok1 > U52^13
top > active1 > U631 > tt > U721 > ok1 > U52^13
top > active1 > U631 > tt > U831 > ok1 > U52^13
top > active1 > U731 > ok1 > U52^13
top > active1 > U741 > tt > U223 > ok1 > U52^13
top > active1 > U741 > tt > U252 > ok1 > U52^13
top > active1 > U741 > tt > U322 > ok1 > U52^13
top > active1 > U741 > tt > U422 > ok1 > U52^13
top > active1 > U741 > tt > U442 > ok1 > U52^13
top > active1 > U741 > tt > U542 > isNeList1 > ok1 > U52^13
top > active1 > U741 > tt > U721 > ok1 > U52^13
top > active1 > U741 > tt > U831 > ok1 > U52^13
top > proper1 > _2 > ok1 > U52^13
top > proper1 > nil > U52^13
top > proper1 > U111 > ok1 > U52^13
top > proper1 > U131 > tt > U223 > ok1 > U52^13
top > proper1 > U131 > tt > U252 > ok1 > U52^13
top > proper1 > U131 > tt > U322 > ok1 > U52^13
top > proper1 > U131 > tt > U422 > ok1 > U52^13
top > proper1 > U131 > tt > U442 > ok1 > U52^13
top > proper1 > U131 > tt > U542 > isNeList1 > ok1 > U52^13
top > proper1 > U131 > tt > U721 > ok1 > U52^13
top > proper1 > U131 > tt > U831 > ok1 > U52^13
top > proper1 > U213 > U223 > ok1 > U52^13
top > proper1 > U233 > ok1 > U52^13
top > proper1 > U242 > U252 > ok1 > U52^13
top > proper1 > isList1 > tt > U223 > ok1 > U52^13
top > proper1 > isList1 > tt > U252 > ok1 > U52^13
top > proper1 > isList1 > tt > U322 > ok1 > U52^13
top > proper1 > isList1 > tt > U422 > ok1 > U52^13
top > proper1 > isList1 > tt > U442 > ok1 > U52^13
top > proper1 > isList1 > tt > U542 > isNeList1 > ok1 > U52^13
top > proper1 > isList1 > tt > U721 > ok1 > U52^13
top > proper1 > isList1 > tt > U831 > ok1 > U52^13
top > proper1 > U311 > U322 > ok1 > U52^13
top > proper1 > U413 > U422 > ok1 > U52^13
top > proper1 > U432 > U442 > ok1 > U52^13
top > proper1 > U512 > ok1 > U52^13
top > proper1 > U523 > ok1 > U52^13
top > proper1 > U631 > tt > U223 > ok1 > U52^13
top > proper1 > U631 > tt > U252 > ok1 > U52^13
top > proper1 > U631 > tt > U322 > ok1 > U52^13
top > proper1 > U631 > tt > U422 > ok1 > U52^13
top > proper1 > U631 > tt > U442 > ok1 > U52^13
top > proper1 > U631 > tt > U542 > isNeList1 > ok1 > U52^13
top > proper1 > U631 > tt > U721 > ok1 > U52^13
top > proper1 > U631 > tt > U831 > ok1 > U52^13
top > proper1 > U731 > ok1 > U52^13
top > proper1 > isPal1 > tt > U223 > ok1 > U52^13
top > proper1 > isPal1 > tt > U252 > ok1 > U52^13
top > proper1 > isPal1 > tt > U322 > ok1 > U52^13
top > proper1 > isPal1 > tt > U422 > ok1 > U52^13
top > proper1 > isPal1 > tt > U442 > ok1 > U52^13
top > proper1 > isPal1 > tt > U542 > isNeList1 > ok1 > U52^13
top > proper1 > isPal1 > tt > U721 > ok1 > U52^13
top > proper1 > isPal1 > tt > U831 > ok1 > U52^13
top > proper1 > U741 > tt > U223 > ok1 > U52^13
top > proper1 > U741 > tt > U252 > ok1 > U52^13
top > proper1 > U741 > tt > U322 > ok1 > U52^13
top > proper1 > U741 > tt > U422 > ok1 > U52^13
top > proper1 > U741 > tt > U442 > ok1 > U52^13
top > proper1 > U741 > tt > U542 > isNeList1 > ok1 > U52^13
top > proper1 > U741 > tt > U721 > ok1 > U52^13
top > proper1 > U741 > tt > U831 > ok1 > U52^13
top > proper1 > a > ok1 > U52^13
top > proper1 > e > ok1 > U52^13
top > proper1 > o > ok1 > U52^13
top > proper1 > u > ok1 > U52^13

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

(149) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(150) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U521(mark(X1), X2, X3) → U521(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U521(x1, x2, x3)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1 > ok
active1 > _2 > isQid > tt > ok
active1 > U111 > U121 > mark1 > ok
active1 > U111 > isPalListKind > mark1 > ok
active1 > U111 > isPalListKind > tt > ok
active1 > U131 > mark1 > ok
active1 > U131 > tt > ok
active1 > U231 > U241 > mark1 > ok
active1 > U231 > U241 > isList > tt > ok
active1 > U251 > mark1 > ok
active1 > U251 > isList > tt > ok
active1 > U261 > mark1 > ok
active1 > U261 > tt > ok
active1 > U451 > isNeList > U311 > mark1 > ok
active1 > U531 > mark1 > ok
active1 > U711 > isPalListKind > mark1 > ok
active1 > U711 > isPalListKind > tt > ok
active1 > U731 > U741 > mark1 > ok
active1 > U731 > U741 > tt > ok
active1 > isPal > tt > ok
active1 > U831 > mark1 > ok
active1 > U831 > tt > ok
active1 > isNePal > isPalListKind > mark1 > ok
active1 > isNePal > isPalListKind > tt > ok
active1 > isNePal > isQid > tt > ok
active1 > U911 > mark1 > ok
nil > ok
a > ok
e > ok
i > ok
o > ok
u > tt > ok
top > ok

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

(151) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(152) PisEmptyProof (EQUIVALENT transformation)

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

(153) TRUE

(154) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(155) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(ok(X1), ok(X2), ok(X3)) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  x3
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  x2
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x2, x3)
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  x2
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x2)
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
top > active1 > _2 > isQid1 > ok1
top > active1 > _2 > U512 > isPalListKind1 > ok1
top > active1 > _2 > U512 > U523 > ok1
top > active1 > U112 > U122 > U131 > ok1
top > active1 > U112 > isPalListKind1 > ok1
top > active1 > U213 > isPalListKind1 > ok1
top > active1 > U213 > U223 > ok1
top > active1 > U232 > isPalListKind1 > ok1
top > active1 > U232 > U243 > ok1
top > active1 > U312 > isPalListKind1 > ok1
top > active1 > U322 > isQid1 > ok1
top > active1 > U331 > tt > isPalListKind1 > ok1
top > active1 > U331 > tt > U131 > ok1
top > active1 > U331 > tt > U223 > ok1
top > active1 > U331 > tt > U243 > ok1
top > active1 > U331 > tt > U252 > ok1
top > active1 > U331 > tt > isQid1 > ok1
top > active1 > U331 > tt > U461 > ok1
top > active1 > U331 > tt > U523 > ok1
top > active1 > U331 > tt > U561 > ok1
top > active1 > U413 > U423 > U433 > isPalListKind1 > ok1
top > active1 > U443 > ok1
top > active1 > U532 > isPalListKind1 > ok1
top > active1 > U612 > isPalListKind1 > ok1
top > active1 > U612 > U622 > isQid1 > ok1
top > active1 > U741 > tt > isPalListKind1 > ok1
top > active1 > U741 > tt > U131 > ok1
top > active1 > U741 > tt > U223 > ok1
top > active1 > U741 > tt > U243 > ok1
top > active1 > U741 > tt > U252 > ok1
top > active1 > U741 > tt > isQid1 > ok1
top > active1 > U741 > tt > U461 > ok1
top > active1 > U741 > tt > U523 > ok1
top > active1 > U741 > tt > U561 > ok1
top > active1 > U812 > ok1
top > active1 > U821 > ok1
top > active1 > U912 > isPalListKind1 > ok1
top > proper1 > _2 > isQid1 > ok1
top > proper1 > _2 > U512 > isPalListKind1 > ok1
top > proper1 > _2 > U512 > U523 > ok1
top > proper1 > nil
top > proper1 > U112 > U122 > U131 > ok1
top > proper1 > U112 > isPalListKind1 > ok1
top > proper1 > U213 > isPalListKind1 > ok1
top > proper1 > U213 > U223 > ok1
top > proper1 > U232 > isPalListKind1 > ok1
top > proper1 > U232 > U243 > ok1
top > proper1 > U312 > isPalListKind1 > ok1
top > proper1 > U322 > isQid1 > ok1
top > proper1 > U331 > tt > isPalListKind1 > ok1
top > proper1 > U331 > tt > U131 > ok1
top > proper1 > U331 > tt > U223 > ok1
top > proper1 > U331 > tt > U243 > ok1
top > proper1 > U331 > tt > U252 > ok1
top > proper1 > U331 > tt > isQid1 > ok1
top > proper1 > U331 > tt > U461 > ok1
top > proper1 > U331 > tt > U523 > ok1
top > proper1 > U331 > tt > U561 > ok1
top > proper1 > U413 > U423 > U433 > isPalListKind1 > ok1
top > proper1 > U443 > ok1
top > proper1 > U532 > isPalListKind1 > ok1
top > proper1 > U612 > isPalListKind1 > ok1
top > proper1 > U612 > U622 > isQid1 > ok1
top > proper1 > U741 > tt > isPalListKind1 > ok1
top > proper1 > U741 > tt > U131 > ok1
top > proper1 > U741 > tt > U223 > ok1
top > proper1 > U741 > tt > U243 > ok1
top > proper1 > U741 > tt > U252 > ok1
top > proper1 > U741 > tt > isQid1 > ok1
top > proper1 > U741 > tt > U461 > ok1
top > proper1 > U741 > tt > U523 > ok1
top > proper1 > U741 > tt > U561 > ok1
top > proper1 > U812 > ok1
top > proper1 > U821 > ok1
top > proper1 > U912 > isPalListKind1 > ok1
top > proper1 > a > tt > isPalListKind1 > ok1
top > proper1 > a > tt > U131 > ok1
top > proper1 > a > tt > U223 > ok1
top > proper1 > a > tt > U243 > ok1
top > proper1 > a > tt > U252 > ok1
top > proper1 > a > tt > isQid1 > ok1
top > proper1 > a > tt > U461 > ok1
top > proper1 > a > tt > U523 > ok1
top > proper1 > a > tt > U561 > ok1
top > proper1 > e
top > proper1 > i > ok1
top > proper1 > o > ok1
top > proper1 > u > ok1

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

(156) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(157) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U511(mark(X1), X2, X3) → U511(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U511(x1, x2, x3)  =  U511(x1, x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
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)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U443 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U452 > isNeList1
active1 > U131 > tt > U533 > mark1
active1 > U131 > tt > U741 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U223 > mark1
active1 > U233 > U243 > mark1
active1 > U252 > mark1
active1 > isList1 > U112 > U122 > mark1
active1 > isList1 > U112 > U122 > isNeList1
active1 > isList1 > isPalListKind > tt > U243 > mark1
active1 > isList1 > isPalListKind > tt > U423 > mark1
active1 > isList1 > isPalListKind > tt > U443 > mark1
active1 > isList1 > isPalListKind > tt > U452 > mark1
active1 > isList1 > isPalListKind > tt > U452 > isNeList1
active1 > isList1 > isPalListKind > tt > U533 > mark1
active1 > isList1 > isPalListKind > tt > U741 > mark1
active1 > isList1 > isPalListKind > tt > U831 > mark1
active1 > isList1 > isPalListKind > U911 > mark1
active1 > isList1 > U213 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U433 > U443 > mark1
active1 > U513 > U523 > U533 > mark1
active1 > U543 > mark1
active1 > U543 > isNeList1
active1 > U552 > mark1
active1 > U631 > tt > U243 > mark1
active1 > U631 > tt > U423 > mark1
active1 > U631 > tt > U443 > mark1
active1 > U631 > tt > U452 > mark1
active1 > U631 > tt > U452 > isNeList1
active1 > U631 > tt > U533 > mark1
active1 > U631 > tt > U741 > mark1
active1 > U631 > tt > U831 > mark1
active1 > U731 > U741 > mark1
active1 > isPal > tt > U243 > mark1
active1 > isPal > tt > U423 > mark1
active1 > isPal > tt > U443 > mark1
active1 > isPal > tt > U452 > mark1
active1 > isPal > tt > U452 > isNeList1
active1 > isPal > tt > U533 > mark1
active1 > isPal > tt > U741 > mark1
active1 > isPal > tt > U831 > mark1
active1 > isNePal > isQid > mark1
active1 > isNePal > U611 > mark1
active1 > isNePal > U711 > mark1
proper1 > _2 > mark1
proper1 > nil
proper1 > U131 > tt > U243 > mark1
proper1 > U131 > tt > U423 > mark1
proper1 > U131 > tt > U443 > mark1
proper1 > U131 > tt > U452 > mark1
proper1 > U131 > tt > U452 > isNeList1
proper1 > U131 > tt > U533 > mark1
proper1 > U131 > tt > U741 > mark1
proper1 > U131 > tt > U831 > mark1
proper1 > U223 > mark1
proper1 > U233 > U243 > mark1
proper1 > U252 > mark1
proper1 > isList1 > U112 > U122 > mark1
proper1 > isList1 > U112 > U122 > isNeList1
proper1 > isList1 > isPalListKind > tt > U243 > mark1
proper1 > isList1 > isPalListKind > tt > U423 > mark1
proper1 > isList1 > isPalListKind > tt > U443 > mark1
proper1 > isList1 > isPalListKind > tt > U452 > mark1
proper1 > isList1 > isPalListKind > tt > U452 > isNeList1
proper1 > isList1 > isPalListKind > tt > U533 > mark1
proper1 > isList1 > isPalListKind > tt > U741 > mark1
proper1 > isList1 > isPalListKind > tt > U831 > mark1
proper1 > isList1 > isPalListKind > U911 > mark1
proper1 > isList1 > U213 > mark1
proper1 > U312 > mark1
proper1 > U413 > mark1
proper1 > U433 > U443 > mark1
proper1 > U513 > U523 > U533 > mark1
proper1 > U543 > mark1
proper1 > U543 > isNeList1
proper1 > U552 > mark1
proper1 > U631 > tt > U243 > mark1
proper1 > U631 > tt > U423 > mark1
proper1 > U631 > tt > U443 > mark1
proper1 > U631 > tt > U452 > mark1
proper1 > U631 > tt > U452 > isNeList1
proper1 > U631 > tt > U533 > mark1
proper1 > U631 > tt > U741 > mark1
proper1 > U631 > tt > U831 > mark1
proper1 > U731 > U741 > mark1
proper1 > isPal > tt > U243 > mark1
proper1 > isPal > tt > U423 > mark1
proper1 > isPal > tt > U443 > mark1
proper1 > isPal > tt > U452 > mark1
proper1 > isPal > tt > U452 > isNeList1
proper1 > isPal > tt > U533 > mark1
proper1 > isPal > tt > U741 > mark1
proper1 > isPal > tt > U831 > mark1
proper1 > isNePal > isQid > mark1
proper1 > isNePal > U611 > mark1
proper1 > isNePal > U711 > mark1
proper1 > a
proper1 > e > mark1
proper1 > i > tt > U243 > mark1
proper1 > i > tt > U423 > mark1
proper1 > i > tt > U443 > mark1
proper1 > i > tt > U452 > mark1
proper1 > i > tt > U452 > isNeList1
proper1 > i > tt > U533 > mark1
proper1 > i > tt > U741 > mark1
proper1 > i > tt > U831 > mark1
proper1 > o > mark1
proper1 > u > mark1

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

(158) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(159) PisEmptyProof (EQUIVALENT transformation)

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

(160) TRUE

(161) Obligation:

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

U461(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(162) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U461(mark(X)) → U461(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U461(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(163) Obligation:

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

U461(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(164) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U461(ok(X)) → U461(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U461(x1)  =  U461(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(165) Obligation:

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

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

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

(166) PisEmptyProof (EQUIVALENT transformation)

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

(167) TRUE

(168) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(169) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U451(ok(X1), ok(X2)) → U451(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U451(x1, x2)  =  U451(x2)
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  U12(x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  x3
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  U23(x3)
U24(x1, x2, x3)  =  U24(x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
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)  =  U54(x2, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  U82(x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U45^11 > ok1
proper1 > _2 > U413 > ok1
proper1 > _2 > U513 > ok1
proper1 > nil > tt > U121 > ok1
proper1 > nil > tt > U461 > ok1
proper1 > nil > tt > U741 > ok1
proper1 > U131 > tt > U121 > ok1
proper1 > U131 > tt > U461 > ok1
proper1 > U131 > tt > U741 > ok1
proper1 > isNeList1 > U413 > ok1
proper1 > isNeList1 > U513 > ok1
proper1 > U231 > ok1
proper1 > U241 > U251 > isList1 > tt > U121 > ok1
proper1 > U241 > U251 > isList1 > tt > U461 > ok1
proper1 > U241 > U251 > isList1 > tt > U741 > ok1
proper1 > U311 > isPalListKind1 > tt > U121 > ok1
proper1 > U311 > isPalListKind1 > tt > U461 > ok1
proper1 > U311 > isPalListKind1 > tt > U741 > ok1
proper1 > U322 > ok1
proper1 > U331 > tt > U121 > ok1
proper1 > U331 > tt > U461 > ok1
proper1 > U331 > tt > U741 > ok1
proper1 > U423 > isPalListKind1 > tt > U121 > ok1
proper1 > U423 > isPalListKind1 > tt > U461 > ok1
proper1 > U423 > isPalListKind1 > tt > U741 > ok1
proper1 > U423 > U432 > ok1
proper1 > U443 > isList1 > tt > U121 > ok1
proper1 > U443 > isList1 > tt > U461 > ok1
proper1 > U443 > isList1 > tt > U741 > ok1
proper1 > U443 > U452 > U461 > ok1
proper1 > U522 > U533 > ok1
proper1 > U542 > ok1
proper1 > U551 > ok1
proper1 > U612 > ok1
proper1 > U622 > ok1
proper1 > U713 > U722 > ok1
proper1 > U732 > U741 > ok1
proper1 > U821 > U831 > tt > U121 > ok1
proper1 > U821 > U831 > tt > U461 > ok1
proper1 > U821 > U831 > tt > U741 > ok1
proper1 > U911 > U921 > tt > U121 > ok1
proper1 > U911 > U921 > tt > U461 > ok1
proper1 > U911 > U921 > tt > U741 > ok1
proper1 > a > tt > U121 > ok1
proper1 > a > tt > U461 > ok1
proper1 > a > tt > U741 > ok1
proper1 > e > ok1
proper1 > i > ok1
proper1 > o > tt > U121 > ok1
proper1 > o > tt > U461 > ok1
proper1 > o > tt > U741 > ok1
proper1 > u > tt > U121 > ok1
proper1 > u > tt > U461 > ok1
proper1 > u > tt > U741 > ok1
top > active1 > _2 > U413 > ok1
top > active1 > _2 > U513 > ok1
top > active1 > U131 > tt > U121 > ok1
top > active1 > U131 > tt > U461 > ok1
top > active1 > U131 > tt > U741 > ok1
top > active1 > isNeList1 > U413 > ok1
top > active1 > isNeList1 > U513 > ok1
top > active1 > U231 > ok1
top > active1 > U241 > U251 > isList1 > tt > U121 > ok1
top > active1 > U241 > U251 > isList1 > tt > U461 > ok1
top > active1 > U241 > U251 > isList1 > tt > U741 > ok1
top > active1 > U311 > isPalListKind1 > tt > U121 > ok1
top > active1 > U311 > isPalListKind1 > tt > U461 > ok1
top > active1 > U311 > isPalListKind1 > tt > U741 > ok1
top > active1 > U322 > ok1
top > active1 > U331 > tt > U121 > ok1
top > active1 > U331 > tt > U461 > ok1
top > active1 > U331 > tt > U741 > ok1
top > active1 > U423 > isPalListKind1 > tt > U121 > ok1
top > active1 > U423 > isPalListKind1 > tt > U461 > ok1
top > active1 > U423 > isPalListKind1 > tt > U741 > ok1
top > active1 > U423 > U432 > ok1
top > active1 > U443 > isList1 > tt > U121 > ok1
top > active1 > U443 > isList1 > tt > U461 > ok1
top > active1 > U443 > isList1 > tt > U741 > ok1
top > active1 > U443 > U452 > U461 > ok1
top > active1 > U522 > U533 > ok1
top > active1 > U542 > ok1
top > active1 > U551 > ok1
top > active1 > U612 > ok1
top > active1 > U622 > ok1
top > active1 > U713 > U722 > ok1
top > active1 > U732 > U741 > ok1
top > active1 > U821 > U831 > tt > U121 > ok1
top > active1 > U821 > U831 > tt > U461 > ok1
top > active1 > U821 > U831 > tt > U741 > ok1
top > active1 > U911 > U921 > tt > U121 > ok1
top > active1 > U911 > U921 > tt > U461 > ok1
top > active1 > U911 > U921 > tt > U741 > ok1

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

(170) Obligation:

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

U451(mark(X1), X2) → U451(X1, X2)

The TRS R consists of the following rules:

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

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

(171) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U451(mark(X1), X2) → U451(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U451(x1, x2)  =  U451(x1)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
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)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > isQid > ok
active1 > _2 > U411 > mark1
active1 > _2 > U411 > ok
active1 > U121 > mark1
active1 > U121 > ok
active1 > isPalListKind > tt > isQid > ok
active1 > isPalListKind > U911 > mark1
active1 > isPalListKind > U911 > ok
active1 > isNeList > mark1
active1 > isNeList > ok
active1 > U221 > mark1
active1 > U221 > ok
active1 > U231 > U241 > isList > mark1
active1 > U231 > U241 > isList > tt > isQid > ok
active1 > U261 > mark1
active1 > U261 > tt > isQid > ok
active1 > U321 > mark1
active1 > U321 > isQid > ok
active1 > U331 > mark1
active1 > U331 > tt > isQid > ok
active1 > U461 > mark1
active1 > U461 > tt > isQid > ok
active1 > U541 > mark1
active1 > U541 > ok
active1 > U631 > mark1
active1 > U631 > tt > isQid > ok
active1 > U713 > U722 > mark1
active1 > U713 > U722 > ok
active1 > isPal1 > tt > isQid > ok
active1 > isPal1 > U812 > mark1
active1 > isPal1 > U812 > ok
active1 > U822 > mark1
active1 > U822 > ok
active1 > U831 > mark1
active1 > U831 > tt > isQid > ok
proper1 > _2 > isQid > ok
proper1 > _2 > U411 > mark1
proper1 > _2 > U411 > ok
proper1 > nil > ok
proper1 > U121 > mark1
proper1 > U121 > ok
proper1 > isPalListKind > tt > isQid > ok
proper1 > isPalListKind > U911 > mark1
proper1 > isPalListKind > U911 > ok
proper1 > isNeList > mark1
proper1 > isNeList > ok
proper1 > U221 > mark1
proper1 > U221 > ok
proper1 > U231 > U241 > isList > mark1
proper1 > U231 > U241 > isList > tt > isQid > ok
proper1 > U261 > mark1
proper1 > U261 > tt > isQid > ok
proper1 > U321 > mark1
proper1 > U321 > isQid > ok
proper1 > U331 > mark1
proper1 > U331 > tt > isQid > ok
proper1 > U461 > mark1
proper1 > U461 > tt > isQid > ok
proper1 > U541 > mark1
proper1 > U541 > ok
proper1 > U631 > mark1
proper1 > U631 > tt > isQid > ok
proper1 > U713 > U722 > mark1
proper1 > U713 > U722 > ok
proper1 > isPal1 > tt > isQid > ok
proper1 > isPal1 > U812 > mark1
proper1 > isPal1 > U812 > ok
proper1 > U822 > mark1
proper1 > U822 > ok
proper1 > U831 > mark1
proper1 > U831 > tt > isQid > ok
proper1 > a
proper1 > e
proper1 > i > ok
proper1 > o > mark1
proper1 > o > tt > isQid > ok
proper1 > u > mark1
proper1 > u > tt > isQid > ok

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

(172) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(173) PisEmptyProof (EQUIVALENT transformation)

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

(174) TRUE

(175) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(176) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(ok(X1), ok(X2), ok(X3)) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  U441(x1, x2, x3)
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x2)
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
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(x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, 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)  =  x2
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
i > tt > U223 > ok1 > U44^13
i > tt > U252 > ok1 > U44^13
i > tt > U322 > ok1 > U44^13
i > tt > U422 > ok1 > U44^13
i > tt > U442 > ok1 > U44^13
i > tt > U542 > isNeList1 > ok1 > U44^13
i > tt > U721 > ok1 > U44^13
i > tt > U831 > ok1 > U44^13
top > active1 > _2 > ok1 > U44^13
top > active1 > U111 > ok1 > U44^13
top > active1 > U131 > tt > U223 > ok1 > U44^13
top > active1 > U131 > tt > U252 > ok1 > U44^13
top > active1 > U131 > tt > U322 > ok1 > U44^13
top > active1 > U131 > tt > U422 > ok1 > U44^13
top > active1 > U131 > tt > U442 > ok1 > U44^13
top > active1 > U131 > tt > U542 > isNeList1 > ok1 > U44^13
top > active1 > U131 > tt > U721 > ok1 > U44^13
top > active1 > U131 > tt > U831 > ok1 > U44^13
top > active1 > U213 > U223 > ok1 > U44^13
top > active1 > U233 > ok1 > U44^13
top > active1 > U242 > U252 > ok1 > U44^13
top > active1 > isList1 > tt > U223 > ok1 > U44^13
top > active1 > isList1 > tt > U252 > ok1 > U44^13
top > active1 > isList1 > tt > U322 > ok1 > U44^13
top > active1 > isList1 > tt > U422 > ok1 > U44^13
top > active1 > isList1 > tt > U442 > ok1 > U44^13
top > active1 > isList1 > tt > U542 > isNeList1 > ok1 > U44^13
top > active1 > isList1 > tt > U721 > ok1 > U44^13
top > active1 > isList1 > tt > U831 > ok1 > U44^13
top > active1 > U311 > U322 > ok1 > U44^13
top > active1 > U413 > U422 > ok1 > U44^13
top > active1 > U432 > U442 > ok1 > U44^13
top > active1 > U512 > ok1 > U44^13
top > active1 > U523 > ok1 > U44^13
top > active1 > U631 > tt > U223 > ok1 > U44^13
top > active1 > U631 > tt > U252 > ok1 > U44^13
top > active1 > U631 > tt > U322 > ok1 > U44^13
top > active1 > U631 > tt > U422 > ok1 > U44^13
top > active1 > U631 > tt > U442 > ok1 > U44^13
top > active1 > U631 > tt > U542 > isNeList1 > ok1 > U44^13
top > active1 > U631 > tt > U721 > ok1 > U44^13
top > active1 > U631 > tt > U831 > ok1 > U44^13
top > active1 > U731 > ok1 > U44^13
top > active1 > U741 > tt > U223 > ok1 > U44^13
top > active1 > U741 > tt > U252 > ok1 > U44^13
top > active1 > U741 > tt > U322 > ok1 > U44^13
top > active1 > U741 > tt > U422 > ok1 > U44^13
top > active1 > U741 > tt > U442 > ok1 > U44^13
top > active1 > U741 > tt > U542 > isNeList1 > ok1 > U44^13
top > active1 > U741 > tt > U721 > ok1 > U44^13
top > active1 > U741 > tt > U831 > ok1 > U44^13
top > proper1 > _2 > ok1 > U44^13
top > proper1 > nil > U44^13
top > proper1 > U111 > ok1 > U44^13
top > proper1 > U131 > tt > U223 > ok1 > U44^13
top > proper1 > U131 > tt > U252 > ok1 > U44^13
top > proper1 > U131 > tt > U322 > ok1 > U44^13
top > proper1 > U131 > tt > U422 > ok1 > U44^13
top > proper1 > U131 > tt > U442 > ok1 > U44^13
top > proper1 > U131 > tt > U542 > isNeList1 > ok1 > U44^13
top > proper1 > U131 > tt > U721 > ok1 > U44^13
top > proper1 > U131 > tt > U831 > ok1 > U44^13
top > proper1 > U213 > U223 > ok1 > U44^13
top > proper1 > U233 > ok1 > U44^13
top > proper1 > U242 > U252 > ok1 > U44^13
top > proper1 > isList1 > tt > U223 > ok1 > U44^13
top > proper1 > isList1 > tt > U252 > ok1 > U44^13
top > proper1 > isList1 > tt > U322 > ok1 > U44^13
top > proper1 > isList1 > tt > U422 > ok1 > U44^13
top > proper1 > isList1 > tt > U442 > ok1 > U44^13
top > proper1 > isList1 > tt > U542 > isNeList1 > ok1 > U44^13
top > proper1 > isList1 > tt > U721 > ok1 > U44^13
top > proper1 > isList1 > tt > U831 > ok1 > U44^13
top > proper1 > U311 > U322 > ok1 > U44^13
top > proper1 > U413 > U422 > ok1 > U44^13
top > proper1 > U432 > U442 > ok1 > U44^13
top > proper1 > U512 > ok1 > U44^13
top > proper1 > U523 > ok1 > U44^13
top > proper1 > U631 > tt > U223 > ok1 > U44^13
top > proper1 > U631 > tt > U252 > ok1 > U44^13
top > proper1 > U631 > tt > U322 > ok1 > U44^13
top > proper1 > U631 > tt > U422 > ok1 > U44^13
top > proper1 > U631 > tt > U442 > ok1 > U44^13
top > proper1 > U631 > tt > U542 > isNeList1 > ok1 > U44^13
top > proper1 > U631 > tt > U721 > ok1 > U44^13
top > proper1 > U631 > tt > U831 > ok1 > U44^13
top > proper1 > U731 > ok1 > U44^13
top > proper1 > isPal1 > tt > U223 > ok1 > U44^13
top > proper1 > isPal1 > tt > U252 > ok1 > U44^13
top > proper1 > isPal1 > tt > U322 > ok1 > U44^13
top > proper1 > isPal1 > tt > U422 > ok1 > U44^13
top > proper1 > isPal1 > tt > U442 > ok1 > U44^13
top > proper1 > isPal1 > tt > U542 > isNeList1 > ok1 > U44^13
top > proper1 > isPal1 > tt > U721 > ok1 > U44^13
top > proper1 > isPal1 > tt > U831 > ok1 > U44^13
top > proper1 > U741 > tt > U223 > ok1 > U44^13
top > proper1 > U741 > tt > U252 > ok1 > U44^13
top > proper1 > U741 > tt > U322 > ok1 > U44^13
top > proper1 > U741 > tt > U422 > ok1 > U44^13
top > proper1 > U741 > tt > U442 > ok1 > U44^13
top > proper1 > U741 > tt > U542 > isNeList1 > ok1 > U44^13
top > proper1 > U741 > tt > U721 > ok1 > U44^13
top > proper1 > U741 > tt > U831 > ok1 > U44^13
top > proper1 > a > ok1 > U44^13
top > proper1 > e > ok1 > U44^13
top > proper1 > o > ok1 > U44^13
top > proper1 > u > ok1 > U44^13

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

(177) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(178) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U441(mark(X1), X2, X3) → U441(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U441(x1, x2, x3)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1 > ok
active1 > _2 > isQid > tt > ok
active1 > U111 > U121 > mark1 > ok
active1 > U111 > isPalListKind > mark1 > ok
active1 > U111 > isPalListKind > tt > ok
active1 > U131 > mark1 > ok
active1 > U131 > tt > ok
active1 > U231 > U241 > mark1 > ok
active1 > U231 > U241 > isList > tt > ok
active1 > U251 > mark1 > ok
active1 > U251 > isList > tt > ok
active1 > U261 > mark1 > ok
active1 > U261 > tt > ok
active1 > U451 > isNeList > U311 > mark1 > ok
active1 > U531 > mark1 > ok
active1 > U711 > isPalListKind > mark1 > ok
active1 > U711 > isPalListKind > tt > ok
active1 > U731 > U741 > mark1 > ok
active1 > U731 > U741 > tt > ok
active1 > isPal > tt > ok
active1 > U831 > mark1 > ok
active1 > U831 > tt > ok
active1 > isNePal > isPalListKind > mark1 > ok
active1 > isNePal > isPalListKind > tt > ok
active1 > isNePal > isQid > tt > ok
active1 > U911 > mark1 > ok
nil > ok
a > ok
e > ok
i > ok
o > ok
u > tt > ok
top > ok

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

(179) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(180) PisEmptyProof (EQUIVALENT transformation)

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

(181) TRUE

(182) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(183) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(mark(X1), X2, X3) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x1, x3)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  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, x2)
U33(x1)  =  U33(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U122 > mark1
active1 > U131 > mark1
active1 > U131 > tt
active1 > U213 > isPalListKind > mark1
active1 > U213 > isPalListKind > tt
active1 > U213 > U223 > mark1
active1 > U233 > isPalListKind > mark1
active1 > U233 > isPalListKind > tt
active1 > U243 > mark1
active1 > U243 > isList1
active1 > U252 > isList1
active1 > U252 > U261 > mark1
active1 > U252 > U261 > tt
active1 > U312 > mark1
active1 > U322 > mark1
active1 > U331 > mark1
active1 > U331 > tt
active1 > isQid > mark1
active1 > isQid > tt
active1 > U413 > U423 > isPalListKind > mark1
active1 > U413 > U423 > isPalListKind > tt
active1 > U433 > isPalListKind > mark1
active1 > U433 > isPalListKind > tt
active1 > U433 > U443 > isList1
active1 > U433 > U443 > U452 > mark1
active1 > U513 > U523 > isPalListKind > mark1
active1 > U513 > U523 > isPalListKind > tt
active1 > U533 > isPalListKind > mark1
active1 > U533 > isPalListKind > tt
active1 > U543 > mark1
active1 > U552 > isList1
active1 > U552 > U561 > mark1
active1 > U552 > U561 > tt
active1 > U612 > isPalListKind > mark1
active1 > U612 > isPalListKind > tt
active1 > U631 > mark1
active1 > U631 > tt
active1 > U713 > isPalListKind > mark1
active1 > U713 > isPalListKind > tt
active1 > U722 > isPal1 > isPalListKind > mark1
active1 > U722 > isPal1 > isPalListKind > tt
active1 > U722 > isPal1 > U812 > mark1
active1 > U731 > isPalListKind > mark1
active1 > U731 > isPalListKind > tt
active1 > U731 > U741 > mark1
active1 > U731 > U741 > tt
active1 > U822 > mark1
active1 > U831 > mark1
active1 > U831 > tt
active1 > U911 > isPalListKind > mark1
active1 > U911 > isPalListKind > tt
a > mark1
a > tt
o > mark1
o > tt
u > mark1
u > tt

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

(184) Obligation:

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

U431(ok(X1), ok(X2), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(185) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U431(ok(X1), ok(X2), ok(X3)) → U431(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U431(x1, x2, x3)  =  U431(x3)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  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, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U513 > isPalListKind1 > ok1
active1 > _2 > U513 > isPalListKind1 > mark1
active1 > tt > U131 > ok1
active1 > tt > U131 > mark1
active1 > tt > U223 > ok1
active1 > tt > U223 > mark1
active1 > tt > U233 > isPalListKind1 > ok1
active1 > tt > U233 > isPalListKind1 > mark1
active1 > tt > U233 > U243 > ok1
active1 > tt > U233 > U243 > mark1
active1 > tt > U252 > ok1
active1 > tt > U252 > mark1
active1 > tt > U261 > ok1
active1 > tt > U261 > mark1
active1 > tt > U322 > ok1
active1 > tt > U322 > mark1
active1 > tt > U331 > ok1
active1 > tt > U331 > mark1
active1 > tt > U423 > U433 > isPalListKind1 > ok1
active1 > tt > U423 > U433 > isPalListKind1 > mark1
active1 > tt > U443 > ok1
active1 > tt > U443 > mark1
active1 > tt > U452 > ok1
active1 > tt > U452 > mark1
active1 > tt > U523 > U533 > isPalListKind1 > ok1
active1 > tt > U523 > U533 > isPalListKind1 > mark1
active1 > tt > U543 > ok1
active1 > tt > U543 > mark1
active1 > tt > U552 > isList1 > U112 > U122 > ok1
active1 > tt > U552 > isList1 > U112 > U122 > mark1
active1 > tt > U552 > isList1 > U112 > isPalListKind1 > ok1
active1 > tt > U552 > isList1 > U112 > isPalListKind1 > mark1
active1 > tt > U552 > U561 > ok1
active1 > tt > U552 > U561 > mark1
active1 > tt > U622 > ok1
active1 > tt > U622 > mark1
active1 > tt > U722 > ok1
active1 > tt > U722 > mark1
active1 > tt > U732 > isPalListKind1 > ok1
active1 > tt > U732 > isPalListKind1 > mark1
active1 > tt > U741 > ok1
active1 > tt > U741 > mark1
active1 > tt > U822 > U831 > ok1
active1 > tt > U822 > U831 > mark1
active1 > tt > U921 > ok1
active1 > tt > U921 > mark1
active1 > U213 > isPalListKind1 > ok1
active1 > U213 > isPalListKind1 > mark1
active1 > U213 > U223 > ok1
active1 > U213 > U223 > mark1
active1 > U312 > isPalListKind1 > ok1
active1 > U312 > isPalListKind1 > mark1
active1 > U312 > U322 > ok1
active1 > U312 > U322 > mark1
active1 > U413 > isPalListKind1 > ok1
active1 > U413 > isPalListKind1 > mark1
active1 > U612 > ok1
active1 > U612 > mark1
active1 > U713 > isPalListKind1 > ok1
active1 > U713 > isPalListKind1 > mark1
active1 > U713 > U722 > ok1
active1 > U713 > U722 > mark1
active1 > U812 > isPalListKind1 > ok1
active1 > U812 > isPalListKind1 > mark1
active1 > U912 > isPalListKind1 > ok1
active1 > U912 > isPalListKind1 > mark1
active1 > U912 > U921 > ok1
active1 > U912 > U921 > mark1
i > ok1
i > mark1
u > ok1
u > mark1
top > proper1 > _2 > U513 > isPalListKind1 > ok1
top > proper1 > _2 > U513 > isPalListKind1 > mark1
top > proper1 > nil > ok1
top > proper1 > nil > mark1
top > proper1 > U131 > ok1
top > proper1 > U131 > mark1
top > proper1 > U213 > isPalListKind1 > ok1
top > proper1 > U213 > isPalListKind1 > mark1
top > proper1 > U213 > U223 > ok1
top > proper1 > U213 > U223 > mark1
top > proper1 > U233 > isPalListKind1 > ok1
top > proper1 > U233 > isPalListKind1 > mark1
top > proper1 > U233 > U243 > ok1
top > proper1 > U233 > U243 > mark1
top > proper1 > U252 > ok1
top > proper1 > U252 > mark1
top > proper1 > U261 > ok1
top > proper1 > U261 > mark1
top > proper1 > U312 > isPalListKind1 > ok1
top > proper1 > U312 > isPalListKind1 > mark1
top > proper1 > U312 > U322 > ok1
top > proper1 > U312 > U322 > mark1
top > proper1 > U331 > ok1
top > proper1 > U331 > mark1
top > proper1 > U413 > isPalListKind1 > ok1
top > proper1 > U413 > isPalListKind1 > mark1
top > proper1 > U423 > U433 > isPalListKind1 > ok1
top > proper1 > U423 > U433 > isPalListKind1 > mark1
top > proper1 > U443 > ok1
top > proper1 > U443 > mark1
top > proper1 > U452 > ok1
top > proper1 > U452 > mark1
top > proper1 > U523 > U533 > isPalListKind1 > ok1
top > proper1 > U523 > U533 > isPalListKind1 > mark1
top > proper1 > U543 > ok1
top > proper1 > U543 > mark1
top > proper1 > U552 > isList1 > U112 > U122 > ok1
top > proper1 > U552 > isList1 > U112 > U122 > mark1
top > proper1 > U552 > isList1 > U112 > isPalListKind1 > ok1
top > proper1 > U552 > isList1 > U112 > isPalListKind1 > mark1
top > proper1 > U552 > U561 > ok1
top > proper1 > U552 > U561 > mark1
top > proper1 > U612 > ok1
top > proper1 > U612 > mark1
top > proper1 > U622 > ok1
top > proper1 > U622 > mark1
top > proper1 > U713 > isPalListKind1 > ok1
top > proper1 > U713 > isPalListKind1 > mark1
top > proper1 > U713 > U722 > ok1
top > proper1 > U713 > U722 > mark1
top > proper1 > U732 > isPalListKind1 > ok1
top > proper1 > U732 > isPalListKind1 > mark1
top > proper1 > U741 > ok1
top > proper1 > U741 > mark1
top > proper1 > U812 > isPalListKind1 > ok1
top > proper1 > U812 > isPalListKind1 > mark1
top > proper1 > U822 > U831 > ok1
top > proper1 > U822 > U831 > mark1
top > proper1 > U912 > isPalListKind1 > ok1
top > proper1 > U912 > isPalListKind1 > mark1
top > proper1 > U912 > U921 > ok1
top > proper1 > U912 > U921 > mark1
top > proper1 > a
top > proper1 > e > ok1
top > proper1 > e > mark1
top > proper1 > o > mark1

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

(186) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(187) PisEmptyProof (EQUIVALENT transformation)

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

(188) TRUE

(189) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(190) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(mark(X1), X2, X3) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x1, x3)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  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, x2)
U33(x1)  =  U33(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U122 > mark1
active1 > U131 > mark1
active1 > U131 > tt
active1 > U213 > isPalListKind > mark1
active1 > U213 > isPalListKind > tt
active1 > U213 > U223 > mark1
active1 > U233 > isPalListKind > mark1
active1 > U233 > isPalListKind > tt
active1 > U243 > mark1
active1 > U243 > isList1
active1 > U252 > isList1
active1 > U252 > U261 > mark1
active1 > U252 > U261 > tt
active1 > U312 > mark1
active1 > U322 > mark1
active1 > U331 > mark1
active1 > U331 > tt
active1 > isQid > mark1
active1 > isQid > tt
active1 > U413 > U423 > isPalListKind > mark1
active1 > U413 > U423 > isPalListKind > tt
active1 > U433 > isPalListKind > mark1
active1 > U433 > isPalListKind > tt
active1 > U433 > U443 > isList1
active1 > U433 > U443 > U452 > mark1
active1 > U513 > U523 > isPalListKind > mark1
active1 > U513 > U523 > isPalListKind > tt
active1 > U533 > isPalListKind > mark1
active1 > U533 > isPalListKind > tt
active1 > U543 > mark1
active1 > U552 > isList1
active1 > U552 > U561 > mark1
active1 > U552 > U561 > tt
active1 > U612 > isPalListKind > mark1
active1 > U612 > isPalListKind > tt
active1 > U631 > mark1
active1 > U631 > tt
active1 > U713 > isPalListKind > mark1
active1 > U713 > isPalListKind > tt
active1 > U722 > isPal1 > isPalListKind > mark1
active1 > U722 > isPal1 > isPalListKind > tt
active1 > U722 > isPal1 > U812 > mark1
active1 > U731 > isPalListKind > mark1
active1 > U731 > isPalListKind > tt
active1 > U731 > U741 > mark1
active1 > U731 > U741 > tt
active1 > U822 > mark1
active1 > U831 > mark1
active1 > U831 > tt
active1 > U911 > isPalListKind > mark1
active1 > U911 > isPalListKind > tt
a > mark1
a > tt
o > mark1
o > tt
u > mark1
u > tt

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

(191) Obligation:

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

U421(ok(X1), ok(X2), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(192) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U421(ok(X1), ok(X2), ok(X3)) → U421(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U421(x1, x2, x3)  =  U421(x3)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  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, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U513 > isPalListKind1 > ok1
active1 > _2 > U513 > isPalListKind1 > mark1
active1 > tt > U131 > ok1
active1 > tt > U131 > mark1
active1 > tt > U223 > ok1
active1 > tt > U223 > mark1
active1 > tt > U233 > isPalListKind1 > ok1
active1 > tt > U233 > isPalListKind1 > mark1
active1 > tt > U233 > U243 > ok1
active1 > tt > U233 > U243 > mark1
active1 > tt > U252 > ok1
active1 > tt > U252 > mark1
active1 > tt > U261 > ok1
active1 > tt > U261 > mark1
active1 > tt > U322 > ok1
active1 > tt > U322 > mark1
active1 > tt > U331 > ok1
active1 > tt > U331 > mark1
active1 > tt > U423 > U433 > isPalListKind1 > ok1
active1 > tt > U423 > U433 > isPalListKind1 > mark1
active1 > tt > U443 > ok1
active1 > tt > U443 > mark1
active1 > tt > U452 > ok1
active1 > tt > U452 > mark1
active1 > tt > U523 > U533 > isPalListKind1 > ok1
active1 > tt > U523 > U533 > isPalListKind1 > mark1
active1 > tt > U543 > ok1
active1 > tt > U543 > mark1
active1 > tt > U552 > isList1 > U112 > U122 > ok1
active1 > tt > U552 > isList1 > U112 > U122 > mark1
active1 > tt > U552 > isList1 > U112 > isPalListKind1 > ok1
active1 > tt > U552 > isList1 > U112 > isPalListKind1 > mark1
active1 > tt > U552 > U561 > ok1
active1 > tt > U552 > U561 > mark1
active1 > tt > U622 > ok1
active1 > tt > U622 > mark1
active1 > tt > U722 > ok1
active1 > tt > U722 > mark1
active1 > tt > U732 > isPalListKind1 > ok1
active1 > tt > U732 > isPalListKind1 > mark1
active1 > tt > U741 > ok1
active1 > tt > U741 > mark1
active1 > tt > U822 > U831 > ok1
active1 > tt > U822 > U831 > mark1
active1 > tt > U921 > ok1
active1 > tt > U921 > mark1
active1 > U213 > isPalListKind1 > ok1
active1 > U213 > isPalListKind1 > mark1
active1 > U213 > U223 > ok1
active1 > U213 > U223 > mark1
active1 > U312 > isPalListKind1 > ok1
active1 > U312 > isPalListKind1 > mark1
active1 > U312 > U322 > ok1
active1 > U312 > U322 > mark1
active1 > U413 > isPalListKind1 > ok1
active1 > U413 > isPalListKind1 > mark1
active1 > U612 > ok1
active1 > U612 > mark1
active1 > U713 > isPalListKind1 > ok1
active1 > U713 > isPalListKind1 > mark1
active1 > U713 > U722 > ok1
active1 > U713 > U722 > mark1
active1 > U812 > isPalListKind1 > ok1
active1 > U812 > isPalListKind1 > mark1
active1 > U912 > isPalListKind1 > ok1
active1 > U912 > isPalListKind1 > mark1
active1 > U912 > U921 > ok1
active1 > U912 > U921 > mark1
i > ok1
i > mark1
u > ok1
u > mark1
top > proper1 > _2 > U513 > isPalListKind1 > ok1
top > proper1 > _2 > U513 > isPalListKind1 > mark1
top > proper1 > nil > ok1
top > proper1 > nil > mark1
top > proper1 > U131 > ok1
top > proper1 > U131 > mark1
top > proper1 > U213 > isPalListKind1 > ok1
top > proper1 > U213 > isPalListKind1 > mark1
top > proper1 > U213 > U223 > ok1
top > proper1 > U213 > U223 > mark1
top > proper1 > U233 > isPalListKind1 > ok1
top > proper1 > U233 > isPalListKind1 > mark1
top > proper1 > U233 > U243 > ok1
top > proper1 > U233 > U243 > mark1
top > proper1 > U252 > ok1
top > proper1 > U252 > mark1
top > proper1 > U261 > ok1
top > proper1 > U261 > mark1
top > proper1 > U312 > isPalListKind1 > ok1
top > proper1 > U312 > isPalListKind1 > mark1
top > proper1 > U312 > U322 > ok1
top > proper1 > U312 > U322 > mark1
top > proper1 > U331 > ok1
top > proper1 > U331 > mark1
top > proper1 > U413 > isPalListKind1 > ok1
top > proper1 > U413 > isPalListKind1 > mark1
top > proper1 > U423 > U433 > isPalListKind1 > ok1
top > proper1 > U423 > U433 > isPalListKind1 > mark1
top > proper1 > U443 > ok1
top > proper1 > U443 > mark1
top > proper1 > U452 > ok1
top > proper1 > U452 > mark1
top > proper1 > U523 > U533 > isPalListKind1 > ok1
top > proper1 > U523 > U533 > isPalListKind1 > mark1
top > proper1 > U543 > ok1
top > proper1 > U543 > mark1
top > proper1 > U552 > isList1 > U112 > U122 > ok1
top > proper1 > U552 > isList1 > U112 > U122 > mark1
top > proper1 > U552 > isList1 > U112 > isPalListKind1 > ok1
top > proper1 > U552 > isList1 > U112 > isPalListKind1 > mark1
top > proper1 > U552 > U561 > ok1
top > proper1 > U552 > U561 > mark1
top > proper1 > U612 > ok1
top > proper1 > U612 > mark1
top > proper1 > U622 > ok1
top > proper1 > U622 > mark1
top > proper1 > U713 > isPalListKind1 > ok1
top > proper1 > U713 > isPalListKind1 > mark1
top > proper1 > U713 > U722 > ok1
top > proper1 > U713 > U722 > mark1
top > proper1 > U732 > isPalListKind1 > ok1
top > proper1 > U732 > isPalListKind1 > mark1
top > proper1 > U741 > ok1
top > proper1 > U741 > mark1
top > proper1 > U812 > isPalListKind1 > ok1
top > proper1 > U812 > isPalListKind1 > mark1
top > proper1 > U822 > U831 > ok1
top > proper1 > U822 > U831 > mark1
top > proper1 > U912 > isPalListKind1 > ok1
top > proper1 > U912 > isPalListKind1 > mark1
top > proper1 > U912 > U921 > ok1
top > proper1 > U912 > U921 > mark1
top > proper1 > a
top > proper1 > e > ok1
top > proper1 > e > mark1
top > proper1 > o > mark1

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

(193) Obligation:

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

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

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

(194) PisEmptyProof (EQUIVALENT transformation)

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

(195) TRUE

(196) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(197) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(ok(X1), ok(X2), ok(X3)) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  x3
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  x2
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x2, x3)
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  x2
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x2)
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
top > active1 > _2 > isQid1 > ok1
top > active1 > _2 > U512 > isPalListKind1 > ok1
top > active1 > _2 > U512 > U523 > ok1
top > active1 > U112 > U122 > U131 > ok1
top > active1 > U112 > isPalListKind1 > ok1
top > active1 > U213 > isPalListKind1 > ok1
top > active1 > U213 > U223 > ok1
top > active1 > U232 > isPalListKind1 > ok1
top > active1 > U232 > U243 > ok1
top > active1 > U312 > isPalListKind1 > ok1
top > active1 > U322 > isQid1 > ok1
top > active1 > U331 > tt > isPalListKind1 > ok1
top > active1 > U331 > tt > U131 > ok1
top > active1 > U331 > tt > U223 > ok1
top > active1 > U331 > tt > U243 > ok1
top > active1 > U331 > tt > U252 > ok1
top > active1 > U331 > tt > isQid1 > ok1
top > active1 > U331 > tt > U461 > ok1
top > active1 > U331 > tt > U523 > ok1
top > active1 > U331 > tt > U561 > ok1
top > active1 > U413 > U423 > U433 > isPalListKind1 > ok1
top > active1 > U443 > ok1
top > active1 > U532 > isPalListKind1 > ok1
top > active1 > U612 > isPalListKind1 > ok1
top > active1 > U612 > U622 > isQid1 > ok1
top > active1 > U741 > tt > isPalListKind1 > ok1
top > active1 > U741 > tt > U131 > ok1
top > active1 > U741 > tt > U223 > ok1
top > active1 > U741 > tt > U243 > ok1
top > active1 > U741 > tt > U252 > ok1
top > active1 > U741 > tt > isQid1 > ok1
top > active1 > U741 > tt > U461 > ok1
top > active1 > U741 > tt > U523 > ok1
top > active1 > U741 > tt > U561 > ok1
top > active1 > U812 > ok1
top > active1 > U821 > ok1
top > active1 > U912 > isPalListKind1 > ok1
top > proper1 > _2 > isQid1 > ok1
top > proper1 > _2 > U512 > isPalListKind1 > ok1
top > proper1 > _2 > U512 > U523 > ok1
top > proper1 > nil
top > proper1 > U112 > U122 > U131 > ok1
top > proper1 > U112 > isPalListKind1 > ok1
top > proper1 > U213 > isPalListKind1 > ok1
top > proper1 > U213 > U223 > ok1
top > proper1 > U232 > isPalListKind1 > ok1
top > proper1 > U232 > U243 > ok1
top > proper1 > U312 > isPalListKind1 > ok1
top > proper1 > U322 > isQid1 > ok1
top > proper1 > U331 > tt > isPalListKind1 > ok1
top > proper1 > U331 > tt > U131 > ok1
top > proper1 > U331 > tt > U223 > ok1
top > proper1 > U331 > tt > U243 > ok1
top > proper1 > U331 > tt > U252 > ok1
top > proper1 > U331 > tt > isQid1 > ok1
top > proper1 > U331 > tt > U461 > ok1
top > proper1 > U331 > tt > U523 > ok1
top > proper1 > U331 > tt > U561 > ok1
top > proper1 > U413 > U423 > U433 > isPalListKind1 > ok1
top > proper1 > U443 > ok1
top > proper1 > U532 > isPalListKind1 > ok1
top > proper1 > U612 > isPalListKind1 > ok1
top > proper1 > U612 > U622 > isQid1 > ok1
top > proper1 > U741 > tt > isPalListKind1 > ok1
top > proper1 > U741 > tt > U131 > ok1
top > proper1 > U741 > tt > U223 > ok1
top > proper1 > U741 > tt > U243 > ok1
top > proper1 > U741 > tt > U252 > ok1
top > proper1 > U741 > tt > isQid1 > ok1
top > proper1 > U741 > tt > U461 > ok1
top > proper1 > U741 > tt > U523 > ok1
top > proper1 > U741 > tt > U561 > ok1
top > proper1 > U812 > ok1
top > proper1 > U821 > ok1
top > proper1 > U912 > isPalListKind1 > ok1
top > proper1 > a > tt > isPalListKind1 > ok1
top > proper1 > a > tt > U131 > ok1
top > proper1 > a > tt > U223 > ok1
top > proper1 > a > tt > U243 > ok1
top > proper1 > a > tt > U252 > ok1
top > proper1 > a > tt > isQid1 > ok1
top > proper1 > a > tt > U461 > ok1
top > proper1 > a > tt > U523 > ok1
top > proper1 > a > tt > U561 > ok1
top > proper1 > e
top > proper1 > i > ok1
top > proper1 > o > ok1
top > proper1 > u > ok1

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

(198) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(199) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U411(mark(X1), X2, X3) → U411(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U411(x1, x2, x3)  =  U411(x1, x2, x3)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
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)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U443 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U452 > isNeList1
active1 > U131 > tt > U533 > mark1
active1 > U131 > tt > U741 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U223 > mark1
active1 > U233 > U243 > mark1
active1 > U252 > mark1
active1 > isList1 > U112 > U122 > mark1
active1 > isList1 > U112 > U122 > isNeList1
active1 > isList1 > isPalListKind > tt > U243 > mark1
active1 > isList1 > isPalListKind > tt > U423 > mark1
active1 > isList1 > isPalListKind > tt > U443 > mark1
active1 > isList1 > isPalListKind > tt > U452 > mark1
active1 > isList1 > isPalListKind > tt > U452 > isNeList1
active1 > isList1 > isPalListKind > tt > U533 > mark1
active1 > isList1 > isPalListKind > tt > U741 > mark1
active1 > isList1 > isPalListKind > tt > U831 > mark1
active1 > isList1 > isPalListKind > U911 > mark1
active1 > isList1 > U213 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U433 > U443 > mark1
active1 > U513 > U523 > U533 > mark1
active1 > U543 > mark1
active1 > U543 > isNeList1
active1 > U552 > mark1
active1 > U631 > tt > U243 > mark1
active1 > U631 > tt > U423 > mark1
active1 > U631 > tt > U443 > mark1
active1 > U631 > tt > U452 > mark1
active1 > U631 > tt > U452 > isNeList1
active1 > U631 > tt > U533 > mark1
active1 > U631 > tt > U741 > mark1
active1 > U631 > tt > U831 > mark1
active1 > U731 > U741 > mark1
active1 > isPal > tt > U243 > mark1
active1 > isPal > tt > U423 > mark1
active1 > isPal > tt > U443 > mark1
active1 > isPal > tt > U452 > mark1
active1 > isPal > tt > U452 > isNeList1
active1 > isPal > tt > U533 > mark1
active1 > isPal > tt > U741 > mark1
active1 > isPal > tt > U831 > mark1
active1 > isNePal > isQid > mark1
active1 > isNePal > U611 > mark1
active1 > isNePal > U711 > mark1
proper1 > _2 > mark1
proper1 > nil
proper1 > U131 > tt > U243 > mark1
proper1 > U131 > tt > U423 > mark1
proper1 > U131 > tt > U443 > mark1
proper1 > U131 > tt > U452 > mark1
proper1 > U131 > tt > U452 > isNeList1
proper1 > U131 > tt > U533 > mark1
proper1 > U131 > tt > U741 > mark1
proper1 > U131 > tt > U831 > mark1
proper1 > U223 > mark1
proper1 > U233 > U243 > mark1
proper1 > U252 > mark1
proper1 > isList1 > U112 > U122 > mark1
proper1 > isList1 > U112 > U122 > isNeList1
proper1 > isList1 > isPalListKind > tt > U243 > mark1
proper1 > isList1 > isPalListKind > tt > U423 > mark1
proper1 > isList1 > isPalListKind > tt > U443 > mark1
proper1 > isList1 > isPalListKind > tt > U452 > mark1
proper1 > isList1 > isPalListKind > tt > U452 > isNeList1
proper1 > isList1 > isPalListKind > tt > U533 > mark1
proper1 > isList1 > isPalListKind > tt > U741 > mark1
proper1 > isList1 > isPalListKind > tt > U831 > mark1
proper1 > isList1 > isPalListKind > U911 > mark1
proper1 > isList1 > U213 > mark1
proper1 > U312 > mark1
proper1 > U413 > mark1
proper1 > U433 > U443 > mark1
proper1 > U513 > U523 > U533 > mark1
proper1 > U543 > mark1
proper1 > U543 > isNeList1
proper1 > U552 > mark1
proper1 > U631 > tt > U243 > mark1
proper1 > U631 > tt > U423 > mark1
proper1 > U631 > tt > U443 > mark1
proper1 > U631 > tt > U452 > mark1
proper1 > U631 > tt > U452 > isNeList1
proper1 > U631 > tt > U533 > mark1
proper1 > U631 > tt > U741 > mark1
proper1 > U631 > tt > U831 > mark1
proper1 > U731 > U741 > mark1
proper1 > isPal > tt > U243 > mark1
proper1 > isPal > tt > U423 > mark1
proper1 > isPal > tt > U443 > mark1
proper1 > isPal > tt > U452 > mark1
proper1 > isPal > tt > U452 > isNeList1
proper1 > isPal > tt > U533 > mark1
proper1 > isPal > tt > U741 > mark1
proper1 > isPal > tt > U831 > mark1
proper1 > isNePal > isQid > mark1
proper1 > isNePal > U611 > mark1
proper1 > isNePal > U711 > mark1
proper1 > a
proper1 > e > mark1
proper1 > i > tt > U243 > mark1
proper1 > i > tt > U423 > mark1
proper1 > i > tt > U443 > mark1
proper1 > i > tt > U452 > mark1
proper1 > i > tt > U452 > isNeList1
proper1 > i > tt > U533 > mark1
proper1 > i > tt > U741 > mark1
proper1 > i > tt > U831 > mark1
proper1 > o > mark1
proper1 > u > mark1

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

(200) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(201) PisEmptyProof (EQUIVALENT transformation)

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

(202) TRUE

(203) Obligation:

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

U331(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(204) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U331(mark(X)) → U331(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U331(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(205) Obligation:

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

U331(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(206) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U331(ok(X)) → U331(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U331(x1)  =  U331(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(207) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(208) PisEmptyProof (EQUIVALENT transformation)

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

(209) TRUE

(210) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(211) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U321(mark(X1), X2) → U321(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U321(x1, x2)  =  U321(x1)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  U55(x1)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U32^11 > mark1
active1 > _2 > U911 > mark1
active1 > isPalListKind > tt > U631 > mark1
active1 > isPalListKind > tt > U822 > mark1
active1 > isPalListKind > U911 > mark1
active1 > U131 > tt > U631 > mark1
active1 > U131 > tt > U822 > mark1
active1 > U221 > mark1
active1 > U231 > mark1
active1 > U241 > isList > U111 > mark1
active1 > U241 > isList > tt > U631 > mark1
active1 > U241 > isList > tt > U822 > mark1
active1 > U251 > isList > U111 > mark1
active1 > U251 > isList > tt > U631 > mark1
active1 > U251 > isList > tt > U822 > mark1
active1 > U261 > tt > U631 > mark1
active1 > U261 > tt > U822 > mark1
active1 > U321 > mark1
active1 > U331 > tt > U631 > mark1
active1 > U331 > tt > U822 > mark1
active1 > U441 > U451 > isNeList > mark1
active1 > U531 > mark1
active1 > U541 > isNeList > mark1
active1 > U541 > U551 > mark1
active1 > U612 > mark1
active1 > U622 > isQid > tt > U631 > mark1
active1 > U622 > isQid > tt > U822 > mark1
active1 > U712 > U722 > mark1
active1 > U812 > U822 > mark1
active1 > U831 > tt > U631 > mark1
active1 > U831 > tt > U822 > mark1
i > tt > U631 > mark1
i > tt > U822 > mark1
proper1 > _2 > U911 > mark1
proper1 > nil > mark1
proper1 > isPalListKind > tt > U631 > mark1
proper1 > isPalListKind > tt > U822 > mark1
proper1 > isPalListKind > U911 > mark1
proper1 > U131 > tt > U631 > mark1
proper1 > U131 > tt > U822 > mark1
proper1 > U221 > mark1
proper1 > U231 > mark1
proper1 > U241 > isList > U111 > mark1
proper1 > U241 > isList > tt > U631 > mark1
proper1 > U241 > isList > tt > U822 > mark1
proper1 > U251 > isList > U111 > mark1
proper1 > U251 > isList > tt > U631 > mark1
proper1 > U251 > isList > tt > U822 > mark1
proper1 > U261 > tt > U631 > mark1
proper1 > U261 > tt > U822 > mark1
proper1 > U321 > mark1
proper1 > U331 > tt > U631 > mark1
proper1 > U331 > tt > U822 > mark1
proper1 > U441 > U451 > isNeList > mark1
proper1 > U531 > mark1
proper1 > U541 > isNeList > mark1
proper1 > U541 > U551 > mark1
proper1 > U612 > mark1
proper1 > U622 > isQid > tt > U631 > mark1
proper1 > U622 > isQid > tt > U822 > mark1
proper1 > U712 > U722 > mark1
proper1 > U812 > U822 > mark1
proper1 > U831 > tt > U631 > mark1
proper1 > U831 > tt > U822 > mark1
proper1 > a > mark1
proper1 > e > tt > U631 > mark1
proper1 > e > tt > U822 > mark1
proper1 > o > tt > U631 > mark1
proper1 > o > tt > U822 > mark1
proper1 > u > tt > U631 > mark1
proper1 > u > tt > U822 > mark1
top > mark1

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

(212) Obligation:

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

U321(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(213) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U321(ok(X1), ok(X2)) → U321(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U321(x1, x2)  =  U321(x1, x2)
ok(x1)  =  ok(x1)
active(x1)  =  x1
__(x1, x2)  =  x2
mark(x1)  =  mark
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  U23(x2)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  x2
U32(x1, x2)  =  U32(x1)
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x2)
U53(x1, x2, x3)  =  x2
U54(x1, x2, x3)  =  x2
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  x1
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U32^12 > mark
proper1 > nil > mark
proper1 > tt > U121 > ok1 > mark
proper1 > tt > isPalListKind1 > ok1 > mark
proper1 > tt > U131 > ok1 > mark
proper1 > tt > U231 > ok1 > mark
proper1 > tt > U241 > U252 > ok1 > mark
proper1 > tt > U321 > isQid1 > ok1 > mark
proper1 > tt > U423 > ok1 > mark
proper1 > tt > U443 > ok1 > mark
proper1 > tt > U452 > ok1 > mark
proper1 > tt > U461 > ok1 > mark
proper1 > tt > U521 > ok1 > mark
proper1 > tt > U552 > U561 > ok1 > mark
proper1 > tt > U621 > isQid1 > ok1 > mark
proper1 > tt > U631 > ok1 > mark
proper1 > tt > U731 > ok1 > mark
proper1 > tt > isPal1 > ok1 > mark
proper1 > tt > U741 > ok1 > mark
proper1 > tt > U921 > ok1 > mark
proper1 > U213 > ok1 > mark
proper1 > U413 > isPalListKind1 > ok1 > mark
proper1 > U413 > U423 > ok1 > mark
proper1 > U512 > isPalListKind1 > ok1 > mark
proper1 > U512 > U521 > ok1 > mark
proper1 > U612 > isPalListKind1 > ok1 > mark
proper1 > U612 > U621 > isQid1 > ok1 > mark
proper1 > U721 > U731 > ok1 > mark
proper1 > U721 > isPal1 > ok1 > mark
proper1 > U812 > ok1 > mark
proper1 > a > mark
proper1 > e > ok1 > mark
proper1 > i > ok1 > mark
proper1 > o > mark
proper1 > u > ok1 > mark
top > mark

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

(214) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(215) PisEmptyProof (EQUIVALENT transformation)

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

(216) TRUE

(217) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(218) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U311(mark(X1), X2) → U311(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U311(x1, x2)  =  U311(x1, x2)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  x1
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  U52(x1)
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  x1
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  U74(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)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
i > tt > U431 > U441 > mark1 > U31^12
i > tt > U431 > U441 > isList
i > tt > U521 > U531 > mark1 > U31^12
i > tt > U741 > mark1 > U31^12
i > tt > U822 > mark1 > U31^12
o > mark1 > U31^12
u > tt > U431 > U441 > mark1 > U31^12
u > tt > U431 > U441 > isList
u > tt > U521 > U531 > mark1 > U31^12
u > tt > U741 > mark1 > U31^12
u > tt > U822 > mark1 > U31^12
top > active1 > _2 > U211 > mark1 > U31^12
top > active1 > _2 > isQid > mark1 > U31^12
top > active1 > U131 > tt > U431 > U441 > mark1 > U31^12
top > active1 > U131 > tt > U431 > U441 > isList
top > active1 > U131 > tt > U521 > U531 > mark1 > U31^12
top > active1 > U131 > tt > U741 > mark1 > U31^12
top > active1 > U131 > tt > U822 > mark1 > U31^12
top > active1 > isNeList > U311 > mark1 > U31^12
top > active1 > U221 > isPalListKind > tt > U431 > U441 > mark1 > U31^12
top > active1 > U221 > isPalListKind > tt > U431 > U441 > isList
top > active1 > U221 > isPalListKind > tt > U521 > U531 > mark1 > U31^12
top > active1 > U221 > isPalListKind > tt > U741 > mark1 > U31^12
top > active1 > U221 > isPalListKind > tt > U822 > mark1 > U31^12
top > active1 > U221 > U231 > mark1 > U31^12
top > active1 > U251 > mark1 > U31^12
top > active1 > U251 > isList
top > active1 > U411 > mark1 > U31^12
top > active1 > U421 > isPalListKind > tt > U431 > U441 > mark1 > U31^12
top > active1 > U421 > isPalListKind > tt > U431 > U441 > isList
top > active1 > U421 > isPalListKind > tt > U521 > U531 > mark1 > U31^12
top > active1 > U421 > isPalListKind > tt > U741 > mark1 > U31^12
top > active1 > U421 > isPalListKind > tt > U822 > mark1 > U31^12
top > active1 > U461 > mark1 > U31^12
top > active1 > U511 > isPalListKind > tt > U431 > U441 > mark1 > U31^12
top > active1 > U511 > isPalListKind > tt > U431 > U441 > isList
top > active1 > U511 > isPalListKind > tt > U521 > U531 > mark1 > U31^12
top > active1 > U511 > isPalListKind > tt > U741 > mark1 > U31^12
top > active1 > U511 > isPalListKind > tt > U822 > mark1 > U31^12
top > active1 > U561 > mark1 > U31^12
top > active1 > U722 > mark1 > U31^12
top > active1 > U812 > isPalListKind > tt > U431 > U441 > mark1 > U31^12
top > active1 > U812 > isPalListKind > tt > U431 > U441 > isList
top > active1 > U812 > isPalListKind > tt > U521 > U531 > mark1 > U31^12
top > active1 > U812 > isPalListKind > tt > U741 > mark1 > U31^12
top > active1 > U812 > isPalListKind > tt > U822 > mark1 > U31^12
top > active1 > U831 > mark1 > U31^12
top > active1 > isNePal1 > isPalListKind > tt > U431 > U441 > mark1 > U31^12
top > active1 > isNePal1 > isPalListKind > tt > U431 > U441 > isList
top > active1 > isNePal1 > isPalListKind > tt > U521 > U531 > mark1 > U31^12
top > active1 > isNePal1 > isPalListKind > tt > U741 > mark1 > U31^12
top > active1 > isNePal1 > isPalListKind > tt > U822 > mark1 > U31^12
top > active1 > isNePal1 > isQid > mark1 > U31^12
top > active1 > isNePal1 > U612 > mark1 > U31^12
top > active1 > isNePal1 > U713 > mark1 > U31^12
top > active1 > U911 > isPalListKind > tt > U431 > U441 > mark1 > U31^12
top > active1 > U911 > isPalListKind > tt > U431 > U441 > isList
top > active1 > U911 > isPalListKind > tt > U521 > U531 > mark1 > U31^12
top > active1 > U911 > isPalListKind > tt > U741 > mark1 > U31^12
top > active1 > U911 > isPalListKind > tt > U822 > mark1 > U31^12
top > active1 > U911 > U921 > tt > U431 > U441 > mark1 > U31^12
top > active1 > U911 > U921 > tt > U431 > U441 > isList
top > active1 > U911 > U921 > tt > U521 > U531 > mark1 > U31^12
top > active1 > U911 > U921 > tt > U741 > mark1 > U31^12
top > active1 > U911 > U921 > tt > U822 > mark1 > U31^12

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

(219) Obligation:

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

U311(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(220) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U311(ok(X1), ok(X2)) → U311(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U311(x1, x2)  =  U311(x1, x2)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  isPalListKind(x1)
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)  =  x3
U24(x1, x2, x3)  =  U24(x1, x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  x2
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(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)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(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)  =  U56(x1)
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U31^12 > ok1
active1 > _2 > U213 > ok1
active1 > isPalListKind1 > tt > ok1
active1 > isPalListKind1 > U911 > ok1
active1 > U131 > tt > ok1
active1 > isNeList1 > U312 > ok1
active1 > U223 > ok1
active1 > U242 > ok1
active1 > U251 > ok1
active1 > isList1 > tt > ok1
active1 > isList1 > U213 > ok1
active1 > U331 > tt > ok1
active1 > U413 > ok1
active1 > U422 > U433 > U443 > ok1
active1 > U452 > ok1
active1 > U461 > tt > ok1
active1 > U512 > U522 > ok1
active1 > U533 > U543 > U552 > U561 > tt > ok1
active1 > U631 > tt > ok1
active1 > U713 > U722 > ok1
active1 > U732 > U741 > tt > ok1
active1 > U812 > U821 > U831 > tt > ok1
active1 > U812 > U821 > isNePal1 > ok1
proper1 > _2 > U213 > ok1
proper1 > nil > ok1
proper1 > isPalListKind1 > tt > ok1
proper1 > isPalListKind1 > U911 > ok1
proper1 > U131 > tt > ok1
proper1 > isNeList1 > U312 > ok1
proper1 > U223 > ok1
proper1 > U242 > ok1
proper1 > U251 > ok1
proper1 > isList1 > tt > ok1
proper1 > isList1 > U213 > ok1
proper1 > U331 > tt > ok1
proper1 > U413 > ok1
proper1 > U422 > U433 > U443 > ok1
proper1 > U452 > ok1
proper1 > U461 > tt > ok1
proper1 > U512 > U522 > ok1
proper1 > U533 > U543 > U552 > U561 > tt > ok1
proper1 > U631 > tt > ok1
proper1 > U713 > U722 > ok1
proper1 > U732 > U741 > tt > ok1
proper1 > U812 > U821 > U831 > tt > ok1
proper1 > U812 > U821 > isNePal1 > ok1
proper1 > a > ok1
proper1 > e > ok1
proper1 > i > ok1
proper1 > o > ok1
proper1 > u > ok1
top > ok1

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

(221) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(222) PisEmptyProof (EQUIVALENT transformation)

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

(223) TRUE

(224) Obligation:

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

U261(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(225) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U261(mark(X)) → U261(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U261(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(226) Obligation:

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

U261(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(227) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U261(ok(X)) → U261(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U261(x1)  =  U261(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(228) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(229) PisEmptyProof (EQUIVALENT transformation)

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

(230) TRUE

(231) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(232) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U251(ok(X1), ok(X2)) → U251(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U251(x1, x2)  =  x2
ok(x1)  =  ok(x1)
mark(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  x3
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  U24(x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(x1)
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)  =  x3
U55(x1, x2)  =  U55(x2)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  x2
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U513 > ok1
active1 > U241 > isList1 > tt > U131 > ok1
active1 > U241 > isList1 > tt > isNeList1 > U513 > ok1
active1 > U241 > isList1 > tt > U251 > U261 > ok1
active1 > U241 > isList1 > tt > U322 > ok1
active1 > U241 > isList1 > tt > U423 > ok1
active1 > U241 > isList1 > tt > U461 > ok1
active1 > U241 > isList1 > tt > U522 > ok1
active1 > U241 > isList1 > tt > U561 > ok1
active1 > U241 > isList1 > tt > U622 > ok1
active1 > U241 > isList1 > tt > U831 > ok1
active1 > U241 > isList1 > tt > isNePal1 > ok1
active1 > U311 > ok1
active1 > U331 > tt > U131 > ok1
active1 > U331 > tt > isNeList1 > U513 > ok1
active1 > U331 > tt > U251 > U261 > ok1
active1 > U331 > tt > U322 > ok1
active1 > U331 > tt > U423 > ok1
active1 > U331 > tt > U461 > ok1
active1 > U331 > tt > U522 > ok1
active1 > U331 > tt > U561 > ok1
active1 > U331 > tt > U622 > ok1
active1 > U331 > tt > U831 > ok1
active1 > U331 > tt > isNePal1 > ok1
active1 > U413 > U423 > ok1
active1 > U432 > U443 > isList1 > tt > U131 > ok1
active1 > U432 > U443 > isList1 > tt > isNeList1 > U513 > ok1
active1 > U432 > U443 > isList1 > tt > U251 > U261 > ok1
active1 > U432 > U443 > isList1 > tt > U322 > ok1
active1 > U432 > U443 > isList1 > tt > U423 > ok1
active1 > U432 > U443 > isList1 > tt > U461 > ok1
active1 > U432 > U443 > isList1 > tt > U522 > ok1
active1 > U432 > U443 > isList1 > tt > U561 > ok1
active1 > U432 > U443 > isList1 > tt > U622 > ok1
active1 > U432 > U443 > isList1 > tt > U831 > ok1
active1 > U432 > U443 > isList1 > tt > isNePal1 > ok1
active1 > U432 > U443 > U452 > isNeList1 > U513 > ok1
active1 > U432 > U443 > U452 > U461 > ok1
active1 > U533 > ok1
active1 > U551 > U561 > ok1
active1 > U612 > ok1
active1 > U713 > U722 > ok1
active1 > U732 > ok1
active1 > U741 > tt > U131 > ok1
active1 > U741 > tt > isNeList1 > U513 > ok1
active1 > U741 > tt > U251 > U261 > ok1
active1 > U741 > tt > U322 > ok1
active1 > U741 > tt > U423 > ok1
active1 > U741 > tt > U461 > ok1
active1 > U741 > tt > U522 > ok1
active1 > U741 > tt > U561 > ok1
active1 > U741 > tt > U622 > ok1
active1 > U741 > tt > U831 > ok1
active1 > U741 > tt > isNePal1 > ok1
active1 > U811 > ok1
active1 > U921 > tt > U131 > ok1
active1 > U921 > tt > isNeList1 > U513 > ok1
active1 > U921 > tt > U251 > U261 > ok1
active1 > U921 > tt > U322 > ok1
active1 > U921 > tt > U423 > ok1
active1 > U921 > tt > U461 > ok1
active1 > U921 > tt > U522 > ok1
active1 > U921 > tt > U561 > ok1
active1 > U921 > tt > U622 > ok1
active1 > U921 > tt > U831 > ok1
active1 > U921 > tt > isNePal1 > ok1
proper1 > _2 > U513 > ok1
proper1 > nil > tt > U131 > ok1
proper1 > nil > tt > isNeList1 > U513 > ok1
proper1 > nil > tt > U251 > U261 > ok1
proper1 > nil > tt > U322 > ok1
proper1 > nil > tt > U423 > ok1
proper1 > nil > tt > U461 > ok1
proper1 > nil > tt > U522 > ok1
proper1 > nil > tt > U561 > ok1
proper1 > nil > tt > U622 > ok1
proper1 > nil > tt > U831 > ok1
proper1 > nil > tt > isNePal1 > ok1
proper1 > U241 > isList1 > tt > U131 > ok1
proper1 > U241 > isList1 > tt > isNeList1 > U513 > ok1
proper1 > U241 > isList1 > tt > U251 > U261 > ok1
proper1 > U241 > isList1 > tt > U322 > ok1
proper1 > U241 > isList1 > tt > U423 > ok1
proper1 > U241 > isList1 > tt > U461 > ok1
proper1 > U241 > isList1 > tt > U522 > ok1
proper1 > U241 > isList1 > tt > U561 > ok1
proper1 > U241 > isList1 > tt > U622 > ok1
proper1 > U241 > isList1 > tt > U831 > ok1
proper1 > U241 > isList1 > tt > isNePal1 > ok1
proper1 > U311 > ok1
proper1 > U331 > tt > U131 > ok1
proper1 > U331 > tt > isNeList1 > U513 > ok1
proper1 > U331 > tt > U251 > U261 > ok1
proper1 > U331 > tt > U322 > ok1
proper1 > U331 > tt > U423 > ok1
proper1 > U331 > tt > U461 > ok1
proper1 > U331 > tt > U522 > ok1
proper1 > U331 > tt > U561 > ok1
proper1 > U331 > tt > U622 > ok1
proper1 > U331 > tt > U831 > ok1
proper1 > U331 > tt > isNePal1 > ok1
proper1 > U413 > U423 > ok1
proper1 > U432 > U443 > isList1 > tt > U131 > ok1
proper1 > U432 > U443 > isList1 > tt > isNeList1 > U513 > ok1
proper1 > U432 > U443 > isList1 > tt > U251 > U261 > ok1
proper1 > U432 > U443 > isList1 > tt > U322 > ok1
proper1 > U432 > U443 > isList1 > tt > U423 > ok1
proper1 > U432 > U443 > isList1 > tt > U461 > ok1
proper1 > U432 > U443 > isList1 > tt > U522 > ok1
proper1 > U432 > U443 > isList1 > tt > U561 > ok1
proper1 > U432 > U443 > isList1 > tt > U622 > ok1
proper1 > U432 > U443 > isList1 > tt > U831 > ok1
proper1 > U432 > U443 > isList1 > tt > isNePal1 > ok1
proper1 > U432 > U443 > U452 > isNeList1 > U513 > ok1
proper1 > U432 > U443 > U452 > U461 > ok1
proper1 > U533 > ok1
proper1 > U551 > U561 > ok1
proper1 > U612 > ok1
proper1 > U713 > U722 > ok1
proper1 > U732 > ok1
proper1 > U741 > tt > U131 > ok1
proper1 > U741 > tt > isNeList1 > U513 > ok1
proper1 > U741 > tt > U251 > U261 > ok1
proper1 > U741 > tt > U322 > ok1
proper1 > U741 > tt > U423 > ok1
proper1 > U741 > tt > U461 > ok1
proper1 > U741 > tt > U522 > ok1
proper1 > U741 > tt > U561 > ok1
proper1 > U741 > tt > U622 > ok1
proper1 > U741 > tt > U831 > ok1
proper1 > U741 > tt > isNePal1 > ok1
proper1 > U811 > ok1
proper1 > U921 > tt > U131 > ok1
proper1 > U921 > tt > isNeList1 > U513 > ok1
proper1 > U921 > tt > U251 > U261 > ok1
proper1 > U921 > tt > U322 > ok1
proper1 > U921 > tt > U423 > ok1
proper1 > U921 > tt > U461 > ok1
proper1 > U921 > tt > U522 > ok1
proper1 > U921 > tt > U561 > ok1
proper1 > U921 > tt > U622 > ok1
proper1 > U921 > tt > U831 > ok1
proper1 > U921 > tt > isNePal1 > ok1
proper1 > a > tt > U131 > ok1
proper1 > a > tt > isNeList1 > U513 > ok1
proper1 > a > tt > U251 > U261 > ok1
proper1 > a > tt > U322 > ok1
proper1 > a > tt > U423 > ok1
proper1 > a > tt > U461 > ok1
proper1 > a > tt > U522 > ok1
proper1 > a > tt > U561 > ok1
proper1 > a > tt > U622 > ok1
proper1 > a > tt > U831 > ok1
proper1 > a > tt > isNePal1 > ok1
proper1 > e > ok1
proper1 > i > ok1
proper1 > o > tt > U131 > ok1
proper1 > o > tt > isNeList1 > U513 > ok1
proper1 > o > tt > U251 > U261 > ok1
proper1 > o > tt > U322 > ok1
proper1 > o > tt > U423 > ok1
proper1 > o > tt > U461 > ok1
proper1 > o > tt > U522 > ok1
proper1 > o > tt > U561 > ok1
proper1 > o > tt > U622 > ok1
proper1 > o > tt > U831 > ok1
proper1 > o > tt > isNePal1 > ok1
proper1 > u > ok1
top > ok1

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

(233) Obligation:

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

U251(mark(X1), X2) → U251(X1, X2)

The TRS R consists of the following rules:

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

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

(234) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U251(mark(X1), X2) → U251(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U251(x1, x2)  =  U251(x1)
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
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)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > isQid > ok
active1 > _2 > U411 > mark1
active1 > _2 > U411 > ok
active1 > U121 > mark1
active1 > U121 > ok
active1 > isPalListKind > tt > isQid > ok
active1 > isPalListKind > U911 > mark1
active1 > isPalListKind > U911 > ok
active1 > isNeList > mark1
active1 > isNeList > ok
active1 > U221 > mark1
active1 > U221 > ok
active1 > U231 > U241 > isList > mark1
active1 > U231 > U241 > isList > tt > isQid > ok
active1 > U261 > mark1
active1 > U261 > tt > isQid > ok
active1 > U321 > mark1
active1 > U321 > isQid > ok
active1 > U331 > mark1
active1 > U331 > tt > isQid > ok
active1 > U461 > mark1
active1 > U461 > tt > isQid > ok
active1 > U541 > mark1
active1 > U541 > ok
active1 > U631 > mark1
active1 > U631 > tt > isQid > ok
active1 > U713 > U722 > mark1
active1 > U713 > U722 > ok
active1 > isPal1 > tt > isQid > ok
active1 > isPal1 > U812 > mark1
active1 > isPal1 > U812 > ok
active1 > U822 > mark1
active1 > U822 > ok
active1 > U831 > mark1
active1 > U831 > tt > isQid > ok
proper1 > _2 > isQid > ok
proper1 > _2 > U411 > mark1
proper1 > _2 > U411 > ok
proper1 > nil > ok
proper1 > U121 > mark1
proper1 > U121 > ok
proper1 > isPalListKind > tt > isQid > ok
proper1 > isPalListKind > U911 > mark1
proper1 > isPalListKind > U911 > ok
proper1 > isNeList > mark1
proper1 > isNeList > ok
proper1 > U221 > mark1
proper1 > U221 > ok
proper1 > U231 > U241 > isList > mark1
proper1 > U231 > U241 > isList > tt > isQid > ok
proper1 > U261 > mark1
proper1 > U261 > tt > isQid > ok
proper1 > U321 > mark1
proper1 > U321 > isQid > ok
proper1 > U331 > mark1
proper1 > U331 > tt > isQid > ok
proper1 > U461 > mark1
proper1 > U461 > tt > isQid > ok
proper1 > U541 > mark1
proper1 > U541 > ok
proper1 > U631 > mark1
proper1 > U631 > tt > isQid > ok
proper1 > U713 > U722 > mark1
proper1 > U713 > U722 > ok
proper1 > isPal1 > tt > isQid > ok
proper1 > isPal1 > U812 > mark1
proper1 > isPal1 > U812 > ok
proper1 > U822 > mark1
proper1 > U822 > ok
proper1 > U831 > mark1
proper1 > U831 > tt > isQid > ok
proper1 > a
proper1 > e
proper1 > i > ok
proper1 > o > mark1
proper1 > o > tt > isQid > ok
proper1 > u > mark1
proper1 > u > tt > isQid > ok

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

(235) Obligation:

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

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

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

(236) PisEmptyProof (EQUIVALENT transformation)

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

(237) TRUE

(238) Obligation:

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

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

The TRS R consists of the following rules:

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

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

(239) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(mark(X1), X2, X3) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x1, x2, x3)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  x1
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > U122 > mark1 > U24^13
nil > tt > U223 > U233 > mark1 > U24^13
nil > tt > U243 > mark1 > U24^13
nil > tt > U252 > mark1 > U24^13
nil > tt > U321 > U331 > mark1 > U24^13
nil > tt > U321 > isQid
nil > tt > U423 > U433 > U443 > mark1 > U24^13
nil > tt > U452 > mark1 > U24^13
nil > tt > U523 > U533 > mark1 > U24^13
nil > tt > U543 > mark1 > U24^13
nil > tt > U552 > isList1 > mark1 > U24^13
nil > tt > U722 > mark1 > U24^13
nil > tt > U822 > mark1 > U24^13
nil > tt > isNePal1 > mark1 > U24^13
nil > tt > isNePal1 > isQid
e > tt > U122 > mark1 > U24^13
e > tt > U223 > U233 > mark1 > U24^13
e > tt > U243 > mark1 > U24^13
e > tt > U252 > mark1 > U24^13
e > tt > U321 > U331 > mark1 > U24^13
e > tt > U321 > isQid
e > tt > U423 > U433 > U443 > mark1 > U24^13
e > tt > U452 > mark1 > U24^13
e > tt > U523 > U533 > mark1 > U24^13
e > tt > U543 > mark1 > U24^13
e > tt > U552 > isList1 > mark1 > U24^13
e > tt > U722 > mark1 > U24^13
e > tt > U822 > mark1 > U24^13
e > tt > isNePal1 > mark1 > U24^13
e > tt > isNePal1 > isQid
o > tt > U122 > mark1 > U24^13
o > tt > U223 > U233 > mark1 > U24^13
o > tt > U243 > mark1 > U24^13
o > tt > U252 > mark1 > U24^13
o > tt > U321 > U331 > mark1 > U24^13
o > tt > U321 > isQid
o > tt > U423 > U433 > U443 > mark1 > U24^13
o > tt > U452 > mark1 > U24^13
o > tt > U523 > U533 > mark1 > U24^13
o > tt > U543 > mark1 > U24^13
o > tt > U552 > isList1 > mark1 > U24^13
o > tt > U722 > mark1 > U24^13
o > tt > U822 > mark1 > U24^13
o > tt > isNePal1 > mark1 > U24^13
o > tt > isNePal1 > isQid
u > tt > U122 > mark1 > U24^13
u > tt > U223 > U233 > mark1 > U24^13
u > tt > U243 > mark1 > U24^13
u > tt > U252 > mark1 > U24^13
u > tt > U321 > U331 > mark1 > U24^13
u > tt > U321 > isQid
u > tt > U423 > U433 > U443 > mark1 > U24^13
u > tt > U452 > mark1 > U24^13
u > tt > U523 > U533 > mark1 > U24^13
u > tt > U543 > mark1 > U24^13
u > tt > U552 > isList1 > mark1 > U24^13
u > tt > U722 > mark1 > U24^13
u > tt > U822 > mark1 > U24^13
u > tt > isNePal1 > mark1 > U24^13
u > tt > isNePal1 > isQid
proper1 > _2 > mark1 > U24^13
proper1 > _2 > isQid
proper1 > U112 > U122 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U122 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U223 > U233 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U243 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U252 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U321 > U331 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U321 > isQid
proper1 > isPalListKind1 > tt > U423 > U433 > U443 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U452 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U523 > U533 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U543 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U552 > isList1 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U722 > mark1 > U24^13
proper1 > isPalListKind1 > tt > U822 > mark1 > U24^13
proper1 > isPalListKind1 > tt > isNePal1 > mark1 > U24^13
proper1 > isPalListKind1 > tt > isNePal1 > isQid
proper1 > isPalListKind1 > U912 > mark1 > U24^13
proper1 > U213 > U223 > U233 > mark1 > U24^13
proper1 > U312 > U321 > U331 > mark1 > U24^13
proper1 > U312 > U321 > isQid
proper1 > U413 > mark1 > U24^13
proper1 > U461 > tt > U122 > mark1 > U24^13
proper1 > U461 > tt > U223 > U233 > mark1 > U24^13
proper1 > U461 > tt > U243 > mark1 > U24^13
proper1 > U461 > tt > U252 > mark1 > U24^13
proper1 > U461 > tt > U321 > U331 > mark1 > U24^13
proper1 > U461 > tt > U321 > isQid
proper1 > U461 > tt > U423 > U433 > U443 > mark1 > U24^13
proper1 > U461 > tt > U452 > mark1 > U24^13
proper1 > U461 > tt > U523 > U533 > mark1 > U24^13
proper1 > U461 > tt > U543 > mark1 > U24^13
proper1 > U461 > tt > U552 > isList1 > mark1 > U24^13
proper1 > U461 > tt > U722 > mark1 > U24^13
proper1 > U461 > tt > U822 > mark1 > U24^13
proper1 > U461 > tt > isNePal1 > mark1 > U24^13
proper1 > U461 > tt > isNePal1 > isQid
proper1 > U513 > mark1 > U24^13
proper1 > U561 > tt > U122 > mark1 > U24^13
proper1 > U561 > tt > U223 > U233 > mark1 > U24^13
proper1 > U561 > tt > U243 > mark1 > U24^13
proper1 > U561 > tt > U252 > mark1 > U24^13
proper1 > U561 > tt > U321 > U331 > mark1 > U24^13
proper1 > U561 > tt > U321 > isQid
proper1 > U561 > tt > U423 > U433 > U443 > mark1 > U24^13
proper1 > U561 > tt > U452 > mark1 > U24^13
proper1 > U561 > tt > U523 > U533 > mark1 > U24^13
proper1 > U561 > tt > U543 > mark1 > U24^13
proper1 > U561 > tt > U552 > isList1 > mark1 > U24^13
proper1 > U561 > tt > U722 > mark1 > U24^13
proper1 > U561 > tt > U822 > mark1 > U24^13
proper1 > U561 > tt > isNePal1 > mark1 > U24^13
proper1 > U561 > tt > isNePal1 > isQid
proper1 > U612 > mark1 > U24^13
proper1 > U713 > U722 > mark1 > U24^13
proper1 > U732 > mark1 > U24^13
proper1 > isPal1 > tt > U122 > mark1 > U24^13
proper1 > isPal1 > tt > U223 > U233 > mark1 > U24^13
proper1 > isPal1 > tt > U243 > mark1 > U24^13
proper1 > isPal1 > tt > U252 > mark1 > U24^13
proper1 > isPal1 > tt > U321 > U331 > mark1 > U24^13
proper1 > isPal1 > tt > U321 > isQid
proper1 > isPal1 > tt > U423 > U433 > U443 > mark1 > U24^13
proper1 > isPal1 > tt > U452 > mark1 > U24^13
proper1 > isPal1 > tt > U523 > U533 > mark1 > U24^13
proper1 > isPal1 > tt > U543 > mark1 > U24^13
proper1 > isPal1 > tt > U552 > isList1 > mark1 > U24^13
proper1 > isPal1 > tt > U722 > mark1 > U24^13
proper1 > isPal1 > tt > U822 > mark1 > U24^13
proper1 > isPal1 > tt > isNePal1 > mark1 > U24^13
proper1 > isPal1 > tt > isNePal1 > isQid
proper1 > isPal1 > U812 > U822 > mark1 > U24^13
proper1 > a
proper1 > i > mark1 > U24^13
top > active1 > _2 > mark1 > U24^13
top > active1 > _2 > isQid
top > active1 > U112 > U122 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U122 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U223 > U233 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U243 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U252 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U321 > U331 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U321 > isQid
top > active1 > isPalListKind1 > tt > U423 > U433 > U443 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U452 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U523 > U533 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U543 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U552 > isList1 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U722 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > U822 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > isNePal1 > mark1 > U24^13
top > active1 > isPalListKind1 > tt > isNePal1 > isQid
top > active1 > isPalListKind1 > U912 > mark1 > U24^13
top > active1 > U213 > U223 > U233 > mark1 > U24^13
top > active1 > U312 > U321 > U331 > mark1 > U24^13
top > active1 > U312 > U321 > isQid
top > active1 > U413 > mark1 > U24^13
top > active1 > U461 > tt > U122 > mark1 > U24^13
top > active1 > U461 > tt > U223 > U233 > mark1 > U24^13
top > active1 > U461 > tt > U243 > mark1 > U24^13
top > active1 > U461 > tt > U252 > mark1 > U24^13
top > active1 > U461 > tt > U321 > U331 > mark1 > U24^13
top > active1 > U461 > tt > U321 > isQid
top > active1 > U461 > tt > U423 > U433 > U443 > mark1 > U24^13
top > active1 > U461 > tt > U452 > mark1 > U24^13
top > active1 > U461 > tt > U523 > U533 > mark1 > U24^13
top > active1 > U461 > tt > U543 > mark1 > U24^13
top > active1 > U461 > tt > U552 > isList1 > mark1 > U24^13
top > active1 > U461 > tt > U722 > mark1 > U24^13
top > active1 > U461 > tt > U822 > mark1 > U24^13
top > active1 > U461 > tt > isNePal1 > mark1 > U24^13
top > active1 > U461 > tt > isNePal1 > isQid
top > active1 > U513 > mark1 > U24^13
top > active1 > U561 > tt > U122 > mark1 > U24^13
top > active1 > U561 > tt > U223 > U233 > mark1 > U24^13
top > active1 > U561 > tt > U243 > mark1 > U24^13
top > active1 > U561 > tt > U252 > mark1 > U24^13
top > active1 > U561 > tt > U321 > U331 > mark1 > U24^13
top > active1 > U561 > tt > U321 > isQid
top > active1 > U561 > tt > U423 > U433 > U443 > mark1 > U24^13
top > active1 > U561 > tt > U452 > mark1 > U24^13
top > active1 > U561 > tt > U523 > U533 > mark1 > U24^13
top > active1 > U561 > tt > U543 > mark1 > U24^13
top > active1 > U561 > tt > U552 > isList1 > mark1 > U24^13
top > active1 > U561 > tt > U722 > mark1 > U24^13
top > active1 > U561 > tt > U822 > mark1 > U24^13
top > active1 > U561 > tt > isNePal1 > mark1 > U24^13
top > active1 > U561 > tt > isNePal1 > isQid
top > active1 > U612 > mark1 > U24^13
top > active1 > U713 > U722 > mark1 > U24^13
top > active1 > U732 > mark1 > U24^13
top > active1 > isPal1 > tt > U122 > mark1 > U24^13
top > active1 > isPal1 > tt > U223 > U233 > mark1 > U24^13
top > active1 > isPal1 > tt > U243 > mark1 > U24^13
top > active1 > isPal1 > tt > U252 > mark1 > U24^13
top > active1 > isPal1 > tt > U321 > U331 > mark1 > U24^13
top > active1 > isPal1 > tt > U321 > isQid
top > active1 > isPal1 > tt > U423 > U433 > U443 > mark1 > U24^13
top > active1 > isPal1 > tt > U452 > mark1 > U24^13
top > active1 > isPal1 > tt > U523 > U533 > mark1 > U24^13
top > active1 > isPal1 > tt > U543 > mark1 > U24^13
top > active1 > isPal1 > tt > U552 > isList1 > mark1 > U24^13
top > active1 > isPal1 > tt > U722 > mark1 > U24^13
top > active1 > isPal1 > tt > U822 > mark1 > U24^13
top > active1 > isPal1 > tt > isNePal1 > mark1 > U24^13
top > active1 > isPal1 > tt > isNePal1 > isQid
top > active1 > isPal1 > U812 > U822 > mark1 > U24^13

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

(240) Obligation:

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

U241(ok(X1), ok(X2), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(241) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U241(ok(X1), ok(X2), ok(X3)) → U241(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U241(x1, x2, x3)  =  U241(x3)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
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, x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  x2
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(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)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x2
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  x2
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
top > active1 > _2 > U213 > isPalListKind1 > ok1
top > active1 > _2 > U213 > U223 > ok1
top > active1 > _2 > U413 > U423 > ok1
top > active1 > _2 > U513 > ok1
top > active1 > U112 > isPalListKind1 > ok1
top > active1 > U122 > U131 > ok1
top > active1 > U122 > isNeList1 > ok1
top > active1 > U331 > tt > U131 > ok1
top > active1 > U331 > tt > U233 > ok1
top > active1 > U331 > tt > U242 > U251 > ok1
top > active1 > U331 > tt > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U331 > tt > isList1 > U213 > U223 > ok1
top > active1 > U331 > tt > U322 > ok1
top > active1 > U331 > tt > isQid1 > ok1
top > active1 > U331 > tt > U423 > ok1
top > active1 > U331 > tt > U433 > ok1
top > active1 > U331 > tt > U452 > isNeList1 > ok1
top > active1 > U331 > tt > U461 > ok1
top > active1 > U331 > tt > U523 > ok1
top > active1 > U331 > tt > U543 > ok1
top > active1 > U331 > tt > isPal1 > isPalListKind1 > ok1
top > active1 > U331 > tt > isNePal1 > isPalListKind1 > ok1
top > active1 > U443 > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U443 > isList1 > U213 > U223 > ok1
top > active1 > U443 > U452 > isNeList1 > ok1
top > active1 > U533 > isPalListKind1 > ok1
top > active1 > U533 > U543 > ok1
top > active1 > U552 > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U552 > isList1 > U213 > U223 > ok1
top > active1 > U631 > tt > U131 > ok1
top > active1 > U631 > tt > U233 > ok1
top > active1 > U631 > tt > U242 > U251 > ok1
top > active1 > U631 > tt > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U631 > tt > isList1 > U213 > U223 > ok1
top > active1 > U631 > tt > U322 > ok1
top > active1 > U631 > tt > isQid1 > ok1
top > active1 > U631 > tt > U423 > ok1
top > active1 > U631 > tt > U433 > ok1
top > active1 > U631 > tt > U452 > isNeList1 > ok1
top > active1 > U631 > tt > U461 > ok1
top > active1 > U631 > tt > U523 > ok1
top > active1 > U631 > tt > U543 > ok1
top > active1 > U631 > tt > isPal1 > isPalListKind1 > ok1
top > active1 > U631 > tt > isNePal1 > isPalListKind1 > ok1
top > active1 > U713 > isPalListKind1 > ok1
top > active1 > U722 > isPal1 > isPalListKind1 > ok1
top > active1 > U822 > isNePal1 > isPalListKind1 > ok1
top > active1 > U831 > tt > U131 > ok1
top > active1 > U831 > tt > U233 > ok1
top > active1 > U831 > tt > U242 > U251 > ok1
top > active1 > U831 > tt > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U831 > tt > isList1 > U213 > U223 > ok1
top > active1 > U831 > tt > U322 > ok1
top > active1 > U831 > tt > isQid1 > ok1
top > active1 > U831 > tt > U423 > ok1
top > active1 > U831 > tt > U433 > ok1
top > active1 > U831 > tt > U452 > isNeList1 > ok1
top > active1 > U831 > tt > U461 > ok1
top > active1 > U831 > tt > U523 > ok1
top > active1 > U831 > tt > U543 > ok1
top > active1 > U831 > tt > isPal1 > isPalListKind1 > ok1
top > active1 > U831 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > _2 > U213 > isPalListKind1 > ok1
top > proper1 > _2 > U213 > U223 > ok1
top > proper1 > _2 > U413 > U423 > ok1
top > proper1 > _2 > U513 > ok1
top > proper1 > nil > tt > U131 > ok1
top > proper1 > nil > tt > U233 > ok1
top > proper1 > nil > tt > U242 > U251 > ok1
top > proper1 > nil > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > nil > tt > isList1 > U213 > U223 > ok1
top > proper1 > nil > tt > U322 > ok1
top > proper1 > nil > tt > isQid1 > ok1
top > proper1 > nil > tt > U423 > ok1
top > proper1 > nil > tt > U433 > ok1
top > proper1 > nil > tt > U452 > isNeList1 > ok1
top > proper1 > nil > tt > U461 > ok1
top > proper1 > nil > tt > U523 > ok1
top > proper1 > nil > tt > U543 > ok1
top > proper1 > nil > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > nil > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > U112 > isPalListKind1 > ok1
top > proper1 > U122 > U131 > ok1
top > proper1 > U122 > isNeList1 > ok1
top > proper1 > U331 > tt > U131 > ok1
top > proper1 > U331 > tt > U233 > ok1
top > proper1 > U331 > tt > U242 > U251 > ok1
top > proper1 > U331 > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U331 > tt > isList1 > U213 > U223 > ok1
top > proper1 > U331 > tt > U322 > ok1
top > proper1 > U331 > tt > isQid1 > ok1
top > proper1 > U331 > tt > U423 > ok1
top > proper1 > U331 > tt > U433 > ok1
top > proper1 > U331 > tt > U452 > isNeList1 > ok1
top > proper1 > U331 > tt > U461 > ok1
top > proper1 > U331 > tt > U523 > ok1
top > proper1 > U331 > tt > U543 > ok1
top > proper1 > U331 > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > U331 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > U443 > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U443 > isList1 > U213 > U223 > ok1
top > proper1 > U443 > U452 > isNeList1 > ok1
top > proper1 > U533 > isPalListKind1 > ok1
top > proper1 > U533 > U543 > ok1
top > proper1 > U552 > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U552 > isList1 > U213 > U223 > ok1
top > proper1 > U631 > tt > U131 > ok1
top > proper1 > U631 > tt > U233 > ok1
top > proper1 > U631 > tt > U242 > U251 > ok1
top > proper1 > U631 > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U631 > tt > isList1 > U213 > U223 > ok1
top > proper1 > U631 > tt > U322 > ok1
top > proper1 > U631 > tt > isQid1 > ok1
top > proper1 > U631 > tt > U423 > ok1
top > proper1 > U631 > tt > U433 > ok1
top > proper1 > U631 > tt > U452 > isNeList1 > ok1
top > proper1 > U631 > tt > U461 > ok1
top > proper1 > U631 > tt > U523 > ok1
top > proper1 > U631 > tt > U543 > ok1
top > proper1 > U631 > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > U631 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > U713 > isPalListKind1 > ok1
top > proper1 > U722 > isPal1 > isPalListKind1 > ok1
top > proper1 > U822 > isNePal1 > isPalListKind1 > ok1
top > proper1 > U831 > tt > U131 > ok1
top > proper1 > U831 > tt > U233 > ok1
top > proper1 > U831 > tt > U242 > U251 > ok1
top > proper1 > U831 > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U831 > tt > isList1 > U213 > U223 > ok1
top > proper1 > U831 > tt > U322 > ok1
top > proper1 > U831 > tt > isQid1 > ok1
top > proper1 > U831 > tt > U423 > ok1
top > proper1 > U831 > tt > U433 > ok1
top > proper1 > U831 > tt > U452 > isNeList1 > ok1
top > proper1 > U831 > tt > U461 > ok1
top > proper1 > U831 > tt > U523 > ok1
top > proper1 > U831 > tt > U543 > ok1
top > proper1 > U831 > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > U831 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > a > ok1
top > proper1 > e
top > proper1 > i
top > proper1 > o > ok1
top > proper1 > u > ok1

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

(242) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(243) PisEmptyProof (EQUIVALENT transformation)

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

(244) TRUE

(245) Obligation:

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

U231(ok(X1), ok(X2), ok(X3)) → U231(X1, X2, X3)
U231(mark(X1), X2, X3) → U231(X1, X2, X3)

The TRS R consists of the following rules:

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

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

(246) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(mark(X1), X2, X3) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x1, x2, x3)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  x1
U62(x1, x2)  =  U62(x1)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  x1
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U74(x1)  =  x1
U81(x1, x2)  =  x1
U82(x1, x2)  =  U82(x1)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  x1
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > _2 > isQid
active1 > U112 > U122 > mark1
active1 > U112 > isPalListKind > mark1
active1 > U213 > mark1
active1 > U223 > isPalListKind > mark1
active1 > U223 > U233 > mark1
active1 > U252 > U261 > tt > U122 > mark1
active1 > U252 > U261 > tt > U233 > mark1
active1 > U252 > U261 > tt > U243 > mark1
active1 > U252 > U261 > tt > U423 > isPalListKind > mark1
active1 > U252 > U261 > tt > U423 > U433 > mark1
active1 > U252 > U261 > tt > U443 > mark1
active1 > U252 > U261 > tt > U543 > isNeList1 > mark1
active1 > U252 > U261 > tt > U543 > U552 > mark1
active1 > U252 > U261 > tt > U561 > mark1
active1 > U252 > U261 > tt > U621 > mark1
active1 > U252 > U261 > tt > U621 > isQid
active1 > U252 > U261 > tt > U821 > mark1
active1 > U252 > U261 > tt > U921 > mark1
active1 > U312 > isPalListKind > mark1
active1 > U322 > mark1
active1 > U322 > isQid
active1 > U413 > U423 > isPalListKind > mark1
active1 > U413 > U423 > U433 > mark1
active1 > U452 > isNeList1 > mark1
active1 > U461 > tt > U122 > mark1
active1 > U461 > tt > U233 > mark1
active1 > U461 > tt > U243 > mark1
active1 > U461 > tt > U423 > isPalListKind > mark1
active1 > U461 > tt > U423 > U433 > mark1
active1 > U461 > tt > U443 > mark1
active1 > U461 > tt > U543 > isNeList1 > mark1
active1 > U461 > tt > U543 > U552 > mark1
active1 > U461 > tt > U561 > mark1
active1 > U461 > tt > U621 > mark1
active1 > U461 > tt > U621 > isQid
active1 > U461 > tt > U821 > mark1
active1 > U461 > tt > U921 > mark1
active1 > U513 > isPalListKind > mark1
active1 > U523 > U533 > isPalListKind > mark1
active1 > U523 > U533 > U543 > isNeList1 > mark1
active1 > U523 > U533 > U543 > U552 > mark1
active1 > U631 > tt > U122 > mark1
active1 > U631 > tt > U233 > mark1
active1 > U631 > tt > U243 > mark1
active1 > U631 > tt > U423 > isPalListKind > mark1
active1 > U631 > tt > U423 > U433 > mark1
active1 > U631 > tt > U443 > mark1
active1 > U631 > tt > U543 > isNeList1 > mark1
active1 > U631 > tt > U543 > U552 > mark1
active1 > U631 > tt > U561 > mark1
active1 > U631 > tt > U621 > mark1
active1 > U631 > tt > U621 > isQid
active1 > U631 > tt > U821 > mark1
active1 > U631 > tt > U921 > mark1
active1 > isPal > tt > U122 > mark1
active1 > isPal > tt > U233 > mark1
active1 > isPal > tt > U243 > mark1
active1 > isPal > tt > U423 > isPalListKind > mark1
active1 > isPal > tt > U423 > U433 > mark1
active1 > isPal > tt > U443 > mark1
active1 > isPal > tt > U543 > isNeList1 > mark1
active1 > isPal > tt > U543 > U552 > mark1
active1 > isPal > tt > U561 > mark1
active1 > isPal > tt > U621 > mark1
active1 > isPal > tt > U621 > isQid
active1 > isPal > tt > U821 > mark1
active1 > isPal > tt > U921 > mark1
active1 > U831 > tt > U122 > mark1
active1 > U831 > tt > U233 > mark1
active1 > U831 > tt > U243 > mark1
active1 > U831 > tt > U423 > isPalListKind > mark1
active1 > U831 > tt > U423 > U433 > mark1
active1 > U831 > tt > U443 > mark1
active1 > U831 > tt > U543 > isNeList1 > mark1
active1 > U831 > tt > U543 > U552 > mark1
active1 > U831 > tt > U561 > mark1
active1 > U831 > tt > U621 > mark1
active1 > U831 > tt > U621 > isQid
active1 > U831 > tt > U821 > mark1
active1 > U831 > tt > U921 > mark1
active1 > isNePal > isPalListKind > mark1
active1 > isNePal > isQid
u > tt > U122 > mark1
u > tt > U233 > mark1
u > tt > U243 > mark1
u > tt > U423 > isPalListKind > mark1
u > tt > U423 > U433 > mark1
u > tt > U443 > mark1
u > tt > U543 > isNeList1 > mark1
u > tt > U543 > U552 > mark1
u > tt > U561 > mark1
u > tt > U621 > mark1
u > tt > U621 > isQid
u > tt > U821 > mark1
u > tt > U921 > mark1
proper1 > _2 > mark1
proper1 > _2 > isQid
proper1 > nil > tt > U122 > mark1
proper1 > nil > tt > U233 > mark1
proper1 > nil > tt > U243 > mark1
proper1 > nil > tt > U423 > isPalListKind > mark1
proper1 > nil > tt > U423 > U433 > mark1
proper1 > nil > tt > U443 > mark1
proper1 > nil > tt > U543 > isNeList1 > mark1
proper1 > nil > tt > U543 > U552 > mark1
proper1 > nil > tt > U561 > mark1
proper1 > nil > tt > U621 > mark1
proper1 > nil > tt > U621 > isQid
proper1 > nil > tt > U821 > mark1
proper1 > nil > tt > U921 > mark1
proper1 > U112 > U122 > mark1
proper1 > U112 > isPalListKind > mark1
proper1 > U213 > mark1
proper1 > U223 > isPalListKind > mark1
proper1 > U223 > U233 > mark1
proper1 > U252 > U261 > tt > U122 > mark1
proper1 > U252 > U261 > tt > U233 > mark1
proper1 > U252 > U261 > tt > U243 > mark1
proper1 > U252 > U261 > tt > U423 > isPalListKind > mark1
proper1 > U252 > U261 > tt > U423 > U433 > mark1
proper1 > U252 > U261 > tt > U443 > mark1
proper1 > U252 > U261 > tt > U543 > isNeList1 > mark1
proper1 > U252 > U261 > tt > U543 > U552 > mark1
proper1 > U252 > U261 > tt > U561 > mark1
proper1 > U252 > U261 > tt > U621 > mark1
proper1 > U252 > U261 > tt > U621 > isQid
proper1 > U252 > U261 > tt > U821 > mark1
proper1 > U252 > U261 > tt > U921 > mark1
proper1 > U312 > isPalListKind > mark1
proper1 > U322 > mark1
proper1 > U322 > isQid
proper1 > U413 > U423 > isPalListKind > mark1
proper1 > U413 > U423 > U433 > mark1
proper1 > U452 > isNeList1 > mark1
proper1 > U461 > tt > U122 > mark1
proper1 > U461 > tt > U233 > mark1
proper1 > U461 > tt > U243 > mark1
proper1 > U461 > tt > U423 > isPalListKind > mark1
proper1 > U461 > tt > U423 > U433 > mark1
proper1 > U461 > tt > U443 > mark1
proper1 > U461 > tt > U543 > isNeList1 > mark1
proper1 > U461 > tt > U543 > U552 > mark1
proper1 > U461 > tt > U561 > mark1
proper1 > U461 > tt > U621 > mark1
proper1 > U461 > tt > U621 > isQid
proper1 > U461 > tt > U821 > mark1
proper1 > U461 > tt > U921 > mark1
proper1 > U513 > isPalListKind > mark1
proper1 > U523 > U533 > isPalListKind > mark1
proper1 > U523 > U533 > U543 > isNeList1 > mark1
proper1 > U523 > U533 > U543 > U552 > mark1
proper1 > U631 > tt > U122 > mark1
proper1 > U631 > tt > U233 > mark1
proper1 > U631 > tt > U243 > mark1
proper1 > U631 > tt > U423 > isPalListKind > mark1
proper1 > U631 > tt > U423 > U433 > mark1
proper1 > U631 > tt > U443 > mark1
proper1 > U631 > tt > U543 > isNeList1 > mark1
proper1 > U631 > tt > U543 > U552 > mark1
proper1 > U631 > tt > U561 > mark1
proper1 > U631 > tt > U621 > mark1
proper1 > U631 > tt > U621 > isQid
proper1 > U631 > tt > U821 > mark1
proper1 > U631 > tt > U921 > mark1
proper1 > isPal > tt > U122 > mark1
proper1 > isPal > tt > U233 > mark1
proper1 > isPal > tt > U243 > mark1
proper1 > isPal > tt > U423 > isPalListKind > mark1
proper1 > isPal > tt > U423 > U433 > mark1
proper1 > isPal > tt > U443 > mark1
proper1 > isPal > tt > U543 > isNeList1 > mark1
proper1 > isPal > tt > U543 > U552 > mark1
proper1 > isPal > tt > U561 > mark1
proper1 > isPal > tt > U621 > mark1
proper1 > isPal > tt > U621 > isQid
proper1 > isPal > tt > U821 > mark1
proper1 > isPal > tt > U921 > mark1
proper1 > U831 > tt > U122 > mark1
proper1 > U831 > tt > U233 > mark1
proper1 > U831 > tt > U243 > mark1
proper1 > U831 > tt > U423 > isPalListKind > mark1
proper1 > U831 > tt > U423 > U433 > mark1
proper1 > U831 > tt > U443 > mark1
proper1 > U831 > tt > U543 > isNeList1 > mark1
proper1 > U831 > tt > U543 > U552 > mark1
proper1 > U831 > tt > U561 > mark1
proper1 > U831 > tt > U621 > mark1
proper1 > U831 > tt > U621 > isQid
proper1 > U831 > tt > U821 > mark1
proper1 > U831 > tt > U921 > mark1
proper1 > isNePal > isPalListKind > mark1
proper1 > isNePal > isQid
proper1 > a
proper1 > e > tt > U122 > mark1
proper1 > e > tt > U233 > mark1
proper1 > e > tt > U243 > mark1
proper1 > e > tt > U423 > isPalListKind > mark1
proper1 > e > tt > U423 > U433 > mark1
proper1 > e > tt > U443 > mark1
proper1 > e > tt > U543 > isNeList1 > mark1
proper1 > e > tt > U543 > U552 > mark1
proper1 > e > tt > U561 > mark1
proper1 > e > tt > U621 > mark1
proper1 > e > tt > U621 > isQid
proper1 > e > tt > U821 > mark1
proper1 > e > tt > U921 > mark1
proper1 > i
proper1 > o > mark1

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

(247) Obligation:

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

U231(ok(X1), ok(X2), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(248) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U231(ok(X1), ok(X2), ok(X3)) → U231(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U231(x1, x2, x3)  =  U231(x3)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  U23(x3)
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x2
U32(x1, x2)  =  U32(x2)
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x3)
U42(x1, x2, x3)  =  x3
U43(x1, x2, x3)  =  U43(x1, x3)
U44(x1, x2, x3)  =  x3
U45(x1, x2)  =  x2
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x3)
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x2
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
a > tt > U131 > ok1
a > tt > U231 > ok1
a > tt > U261 > ok1
a > tt > U461 > ok1
a > tt > U521 > ok1
a > tt > U622 > isQid1 > ok1
a > tt > U622 > U631 > ok1
a > tt > U921 > ok1
top > active1 > _2 > ok1
top > active1 > U112 > ok1
top > active1 > tt > U131 > ok1
top > active1 > tt > U231 > ok1
top > active1 > tt > U261 > ok1
top > active1 > tt > U461 > ok1
top > active1 > tt > U521 > ok1
top > active1 > tt > U622 > isQid1 > ok1
top > active1 > tt > U622 > U631 > ok1
top > active1 > tt > U921 > ok1
top > active1 > U212 > ok1
top > active1 > U251 > U261 > ok1
top > active1 > U321 > isQid1 > ok1
top > active1 > U411 > ok1
top > active1 > U432 > ok1
top > active1 > U513 > U521 > ok1
top > active1 > U612 > U622 > isQid1 > ok1
top > active1 > U612 > U622 > U631 > ok1
top > active1 > U713 > ok1
top > active1 > U722 > ok1
top > active1 > U811 > U822 > ok1
top > active1 > U831 > ok1
top > active1 > U912 > ok1
top > proper1 > _2 > ok1
top > proper1 > nil
top > proper1 > U112 > ok1
top > proper1 > tt > U131 > ok1
top > proper1 > tt > U231 > ok1
top > proper1 > tt > U261 > ok1
top > proper1 > tt > U461 > ok1
top > proper1 > tt > U521 > ok1
top > proper1 > tt > U622 > isQid1 > ok1
top > proper1 > tt > U622 > U631 > ok1
top > proper1 > tt > U921 > ok1
top > proper1 > U212 > ok1
top > proper1 > U251 > U261 > ok1
top > proper1 > U321 > isQid1 > ok1
top > proper1 > U411 > ok1
top > proper1 > U432 > ok1
top > proper1 > U513 > U521 > ok1
top > proper1 > U612 > U622 > isQid1 > ok1
top > proper1 > U612 > U622 > U631 > ok1
top > proper1 > U713 > ok1
top > proper1 > U722 > ok1
top > proper1 > U811 > U822 > ok1
top > proper1 > U831 > ok1
top > proper1 > U912 > ok1
top > proper1 > e
top > proper1 > i > ok1
top > proper1 > o
top > proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(249) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(250) PisEmptyProof (EQUIVALENT transformation)

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

(251) TRUE

(252) Obligation:

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

U221(ok(X1), ok(X2), ok(X3)) → U221(X1, X2, X3)
U221(mark(X1), X2, X3) → U221(X1, X2, X3)

The TRS R consists of the following rules:

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

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

(253) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(mark(X1), X2, X3) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x1, x2, x3)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  x1
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > U122 > mark1 > U22^13
nil > tt > U223 > U233 > mark1 > U22^13
nil > tt > U243 > mark1 > U22^13
nil > tt > U252 > mark1 > U22^13
nil > tt > U321 > U331 > mark1 > U22^13
nil > tt > U321 > isQid
nil > tt > U423 > U433 > U443 > mark1 > U22^13
nil > tt > U452 > mark1 > U22^13
nil > tt > U523 > U533 > mark1 > U22^13
nil > tt > U543 > mark1 > U22^13
nil > tt > U552 > isList1 > mark1 > U22^13
nil > tt > U722 > mark1 > U22^13
nil > tt > U822 > mark1 > U22^13
nil > tt > isNePal1 > mark1 > U22^13
nil > tt > isNePal1 > isQid
e > tt > U122 > mark1 > U22^13
e > tt > U223 > U233 > mark1 > U22^13
e > tt > U243 > mark1 > U22^13
e > tt > U252 > mark1 > U22^13
e > tt > U321 > U331 > mark1 > U22^13
e > tt > U321 > isQid
e > tt > U423 > U433 > U443 > mark1 > U22^13
e > tt > U452 > mark1 > U22^13
e > tt > U523 > U533 > mark1 > U22^13
e > tt > U543 > mark1 > U22^13
e > tt > U552 > isList1 > mark1 > U22^13
e > tt > U722 > mark1 > U22^13
e > tt > U822 > mark1 > U22^13
e > tt > isNePal1 > mark1 > U22^13
e > tt > isNePal1 > isQid
o > tt > U122 > mark1 > U22^13
o > tt > U223 > U233 > mark1 > U22^13
o > tt > U243 > mark1 > U22^13
o > tt > U252 > mark1 > U22^13
o > tt > U321 > U331 > mark1 > U22^13
o > tt > U321 > isQid
o > tt > U423 > U433 > U443 > mark1 > U22^13
o > tt > U452 > mark1 > U22^13
o > tt > U523 > U533 > mark1 > U22^13
o > tt > U543 > mark1 > U22^13
o > tt > U552 > isList1 > mark1 > U22^13
o > tt > U722 > mark1 > U22^13
o > tt > U822 > mark1 > U22^13
o > tt > isNePal1 > mark1 > U22^13
o > tt > isNePal1 > isQid
u > tt > U122 > mark1 > U22^13
u > tt > U223 > U233 > mark1 > U22^13
u > tt > U243 > mark1 > U22^13
u > tt > U252 > mark1 > U22^13
u > tt > U321 > U331 > mark1 > U22^13
u > tt > U321 > isQid
u > tt > U423 > U433 > U443 > mark1 > U22^13
u > tt > U452 > mark1 > U22^13
u > tt > U523 > U533 > mark1 > U22^13
u > tt > U543 > mark1 > U22^13
u > tt > U552 > isList1 > mark1 > U22^13
u > tt > U722 > mark1 > U22^13
u > tt > U822 > mark1 > U22^13
u > tt > isNePal1 > mark1 > U22^13
u > tt > isNePal1 > isQid
proper1 > _2 > mark1 > U22^13
proper1 > _2 > isQid
proper1 > U112 > U122 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U122 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U223 > U233 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U243 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U252 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U321 > U331 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U321 > isQid
proper1 > isPalListKind1 > tt > U423 > U433 > U443 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U452 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U523 > U533 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U543 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U552 > isList1 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U722 > mark1 > U22^13
proper1 > isPalListKind1 > tt > U822 > mark1 > U22^13
proper1 > isPalListKind1 > tt > isNePal1 > mark1 > U22^13
proper1 > isPalListKind1 > tt > isNePal1 > isQid
proper1 > isPalListKind1 > U912 > mark1 > U22^13
proper1 > U213 > U223 > U233 > mark1 > U22^13
proper1 > U312 > U321 > U331 > mark1 > U22^13
proper1 > U312 > U321 > isQid
proper1 > U413 > mark1 > U22^13
proper1 > U461 > tt > U122 > mark1 > U22^13
proper1 > U461 > tt > U223 > U233 > mark1 > U22^13
proper1 > U461 > tt > U243 > mark1 > U22^13
proper1 > U461 > tt > U252 > mark1 > U22^13
proper1 > U461 > tt > U321 > U331 > mark1 > U22^13
proper1 > U461 > tt > U321 > isQid
proper1 > U461 > tt > U423 > U433 > U443 > mark1 > U22^13
proper1 > U461 > tt > U452 > mark1 > U22^13
proper1 > U461 > tt > U523 > U533 > mark1 > U22^13
proper1 > U461 > tt > U543 > mark1 > U22^13
proper1 > U461 > tt > U552 > isList1 > mark1 > U22^13
proper1 > U461 > tt > U722 > mark1 > U22^13
proper1 > U461 > tt > U822 > mark1 > U22^13
proper1 > U461 > tt > isNePal1 > mark1 > U22^13
proper1 > U461 > tt > isNePal1 > isQid
proper1 > U513 > mark1 > U22^13
proper1 > U561 > tt > U122 > mark1 > U22^13
proper1 > U561 > tt > U223 > U233 > mark1 > U22^13
proper1 > U561 > tt > U243 > mark1 > U22^13
proper1 > U561 > tt > U252 > mark1 > U22^13
proper1 > U561 > tt > U321 > U331 > mark1 > U22^13
proper1 > U561 > tt > U321 > isQid
proper1 > U561 > tt > U423 > U433 > U443 > mark1 > U22^13
proper1 > U561 > tt > U452 > mark1 > U22^13
proper1 > U561 > tt > U523 > U533 > mark1 > U22^13
proper1 > U561 > tt > U543 > mark1 > U22^13
proper1 > U561 > tt > U552 > isList1 > mark1 > U22^13
proper1 > U561 > tt > U722 > mark1 > U22^13
proper1 > U561 > tt > U822 > mark1 > U22^13
proper1 > U561 > tt > isNePal1 > mark1 > U22^13
proper1 > U561 > tt > isNePal1 > isQid
proper1 > U612 > mark1 > U22^13
proper1 > U713 > U722 > mark1 > U22^13
proper1 > U732 > mark1 > U22^13
proper1 > isPal1 > tt > U122 > mark1 > U22^13
proper1 > isPal1 > tt > U223 > U233 > mark1 > U22^13
proper1 > isPal1 > tt > U243 > mark1 > U22^13
proper1 > isPal1 > tt > U252 > mark1 > U22^13
proper1 > isPal1 > tt > U321 > U331 > mark1 > U22^13
proper1 > isPal1 > tt > U321 > isQid
proper1 > isPal1 > tt > U423 > U433 > U443 > mark1 > U22^13
proper1 > isPal1 > tt > U452 > mark1 > U22^13
proper1 > isPal1 > tt > U523 > U533 > mark1 > U22^13
proper1 > isPal1 > tt > U543 > mark1 > U22^13
proper1 > isPal1 > tt > U552 > isList1 > mark1 > U22^13
proper1 > isPal1 > tt > U722 > mark1 > U22^13
proper1 > isPal1 > tt > U822 > mark1 > U22^13
proper1 > isPal1 > tt > isNePal1 > mark1 > U22^13
proper1 > isPal1 > tt > isNePal1 > isQid
proper1 > isPal1 > U812 > U822 > mark1 > U22^13
proper1 > a
proper1 > i > mark1 > U22^13
top > active1 > _2 > mark1 > U22^13
top > active1 > _2 > isQid
top > active1 > U112 > U122 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U122 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U223 > U233 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U243 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U252 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U321 > U331 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U321 > isQid
top > active1 > isPalListKind1 > tt > U423 > U433 > U443 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U452 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U523 > U533 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U543 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U552 > isList1 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U722 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > U822 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > isNePal1 > mark1 > U22^13
top > active1 > isPalListKind1 > tt > isNePal1 > isQid
top > active1 > isPalListKind1 > U912 > mark1 > U22^13
top > active1 > U213 > U223 > U233 > mark1 > U22^13
top > active1 > U312 > U321 > U331 > mark1 > U22^13
top > active1 > U312 > U321 > isQid
top > active1 > U413 > mark1 > U22^13
top > active1 > U461 > tt > U122 > mark1 > U22^13
top > active1 > U461 > tt > U223 > U233 > mark1 > U22^13
top > active1 > U461 > tt > U243 > mark1 > U22^13
top > active1 > U461 > tt > U252 > mark1 > U22^13
top > active1 > U461 > tt > U321 > U331 > mark1 > U22^13
top > active1 > U461 > tt > U321 > isQid
top > active1 > U461 > tt > U423 > U433 > U443 > mark1 > U22^13
top > active1 > U461 > tt > U452 > mark1 > U22^13
top > active1 > U461 > tt > U523 > U533 > mark1 > U22^13
top > active1 > U461 > tt > U543 > mark1 > U22^13
top > active1 > U461 > tt > U552 > isList1 > mark1 > U22^13
top > active1 > U461 > tt > U722 > mark1 > U22^13
top > active1 > U461 > tt > U822 > mark1 > U22^13
top > active1 > U461 > tt > isNePal1 > mark1 > U22^13
top > active1 > U461 > tt > isNePal1 > isQid
top > active1 > U513 > mark1 > U22^13
top > active1 > U561 > tt > U122 > mark1 > U22^13
top > active1 > U561 > tt > U223 > U233 > mark1 > U22^13
top > active1 > U561 > tt > U243 > mark1 > U22^13
top > active1 > U561 > tt > U252 > mark1 > U22^13
top > active1 > U561 > tt > U321 > U331 > mark1 > U22^13
top > active1 > U561 > tt > U321 > isQid
top > active1 > U561 > tt > U423 > U433 > U443 > mark1 > U22^13
top > active1 > U561 > tt > U452 > mark1 > U22^13
top > active1 > U561 > tt > U523 > U533 > mark1 > U22^13
top > active1 > U561 > tt > U543 > mark1 > U22^13
top > active1 > U561 > tt > U552 > isList1 > mark1 > U22^13
top > active1 > U561 > tt > U722 > mark1 > U22^13
top > active1 > U561 > tt > U822 > mark1 > U22^13
top > active1 > U561 > tt > isNePal1 > mark1 > U22^13
top > active1 > U561 > tt > isNePal1 > isQid
top > active1 > U612 > mark1 > U22^13
top > active1 > U713 > U722 > mark1 > U22^13
top > active1 > U732 > mark1 > U22^13
top > active1 > isPal1 > tt > U122 > mark1 > U22^13
top > active1 > isPal1 > tt > U223 > U233 > mark1 > U22^13
top > active1 > isPal1 > tt > U243 > mark1 > U22^13
top > active1 > isPal1 > tt > U252 > mark1 > U22^13
top > active1 > isPal1 > tt > U321 > U331 > mark1 > U22^13
top > active1 > isPal1 > tt > U321 > isQid
top > active1 > isPal1 > tt > U423 > U433 > U443 > mark1 > U22^13
top > active1 > isPal1 > tt > U452 > mark1 > U22^13
top > active1 > isPal1 > tt > U523 > U533 > mark1 > U22^13
top > active1 > isPal1 > tt > U543 > mark1 > U22^13
top > active1 > isPal1 > tt > U552 > isList1 > mark1 > U22^13
top > active1 > isPal1 > tt > U722 > mark1 > U22^13
top > active1 > isPal1 > tt > U822 > mark1 > U22^13
top > active1 > isPal1 > tt > isNePal1 > mark1 > U22^13
top > active1 > isPal1 > tt > isNePal1 > isQid
top > active1 > isPal1 > U812 > U822 > mark1 > U22^13

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

(254) Obligation:

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

U221(ok(X1), ok(X2), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(255) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U221(ok(X1), ok(X2), ok(X3)) → U221(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U221(x1, x2, x3)  =  U221(x3)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
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, x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  x2
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(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)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x2
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  x2
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
top > active1 > _2 > U213 > isPalListKind1 > ok1
top > active1 > _2 > U213 > U223 > ok1
top > active1 > _2 > U413 > U423 > ok1
top > active1 > _2 > U513 > ok1
top > active1 > U112 > isPalListKind1 > ok1
top > active1 > U122 > U131 > ok1
top > active1 > U122 > isNeList1 > ok1
top > active1 > U331 > tt > U131 > ok1
top > active1 > U331 > tt > U233 > ok1
top > active1 > U331 > tt > U242 > U251 > ok1
top > active1 > U331 > tt > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U331 > tt > isList1 > U213 > U223 > ok1
top > active1 > U331 > tt > U322 > ok1
top > active1 > U331 > tt > isQid1 > ok1
top > active1 > U331 > tt > U423 > ok1
top > active1 > U331 > tt > U433 > ok1
top > active1 > U331 > tt > U452 > isNeList1 > ok1
top > active1 > U331 > tt > U461 > ok1
top > active1 > U331 > tt > U523 > ok1
top > active1 > U331 > tt > U543 > ok1
top > active1 > U331 > tt > isPal1 > isPalListKind1 > ok1
top > active1 > U331 > tt > isNePal1 > isPalListKind1 > ok1
top > active1 > U443 > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U443 > isList1 > U213 > U223 > ok1
top > active1 > U443 > U452 > isNeList1 > ok1
top > active1 > U533 > isPalListKind1 > ok1
top > active1 > U533 > U543 > ok1
top > active1 > U552 > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U552 > isList1 > U213 > U223 > ok1
top > active1 > U631 > tt > U131 > ok1
top > active1 > U631 > tt > U233 > ok1
top > active1 > U631 > tt > U242 > U251 > ok1
top > active1 > U631 > tt > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U631 > tt > isList1 > U213 > U223 > ok1
top > active1 > U631 > tt > U322 > ok1
top > active1 > U631 > tt > isQid1 > ok1
top > active1 > U631 > tt > U423 > ok1
top > active1 > U631 > tt > U433 > ok1
top > active1 > U631 > tt > U452 > isNeList1 > ok1
top > active1 > U631 > tt > U461 > ok1
top > active1 > U631 > tt > U523 > ok1
top > active1 > U631 > tt > U543 > ok1
top > active1 > U631 > tt > isPal1 > isPalListKind1 > ok1
top > active1 > U631 > tt > isNePal1 > isPalListKind1 > ok1
top > active1 > U713 > isPalListKind1 > ok1
top > active1 > U722 > isPal1 > isPalListKind1 > ok1
top > active1 > U822 > isNePal1 > isPalListKind1 > ok1
top > active1 > U831 > tt > U131 > ok1
top > active1 > U831 > tt > U233 > ok1
top > active1 > U831 > tt > U242 > U251 > ok1
top > active1 > U831 > tt > isList1 > U213 > isPalListKind1 > ok1
top > active1 > U831 > tt > isList1 > U213 > U223 > ok1
top > active1 > U831 > tt > U322 > ok1
top > active1 > U831 > tt > isQid1 > ok1
top > active1 > U831 > tt > U423 > ok1
top > active1 > U831 > tt > U433 > ok1
top > active1 > U831 > tt > U452 > isNeList1 > ok1
top > active1 > U831 > tt > U461 > ok1
top > active1 > U831 > tt > U523 > ok1
top > active1 > U831 > tt > U543 > ok1
top > active1 > U831 > tt > isPal1 > isPalListKind1 > ok1
top > active1 > U831 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > _2 > U213 > isPalListKind1 > ok1
top > proper1 > _2 > U213 > U223 > ok1
top > proper1 > _2 > U413 > U423 > ok1
top > proper1 > _2 > U513 > ok1
top > proper1 > nil > tt > U131 > ok1
top > proper1 > nil > tt > U233 > ok1
top > proper1 > nil > tt > U242 > U251 > ok1
top > proper1 > nil > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > nil > tt > isList1 > U213 > U223 > ok1
top > proper1 > nil > tt > U322 > ok1
top > proper1 > nil > tt > isQid1 > ok1
top > proper1 > nil > tt > U423 > ok1
top > proper1 > nil > tt > U433 > ok1
top > proper1 > nil > tt > U452 > isNeList1 > ok1
top > proper1 > nil > tt > U461 > ok1
top > proper1 > nil > tt > U523 > ok1
top > proper1 > nil > tt > U543 > ok1
top > proper1 > nil > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > nil > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > U112 > isPalListKind1 > ok1
top > proper1 > U122 > U131 > ok1
top > proper1 > U122 > isNeList1 > ok1
top > proper1 > U331 > tt > U131 > ok1
top > proper1 > U331 > tt > U233 > ok1
top > proper1 > U331 > tt > U242 > U251 > ok1
top > proper1 > U331 > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U331 > tt > isList1 > U213 > U223 > ok1
top > proper1 > U331 > tt > U322 > ok1
top > proper1 > U331 > tt > isQid1 > ok1
top > proper1 > U331 > tt > U423 > ok1
top > proper1 > U331 > tt > U433 > ok1
top > proper1 > U331 > tt > U452 > isNeList1 > ok1
top > proper1 > U331 > tt > U461 > ok1
top > proper1 > U331 > tt > U523 > ok1
top > proper1 > U331 > tt > U543 > ok1
top > proper1 > U331 > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > U331 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > U443 > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U443 > isList1 > U213 > U223 > ok1
top > proper1 > U443 > U452 > isNeList1 > ok1
top > proper1 > U533 > isPalListKind1 > ok1
top > proper1 > U533 > U543 > ok1
top > proper1 > U552 > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U552 > isList1 > U213 > U223 > ok1
top > proper1 > U631 > tt > U131 > ok1
top > proper1 > U631 > tt > U233 > ok1
top > proper1 > U631 > tt > U242 > U251 > ok1
top > proper1 > U631 > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U631 > tt > isList1 > U213 > U223 > ok1
top > proper1 > U631 > tt > U322 > ok1
top > proper1 > U631 > tt > isQid1 > ok1
top > proper1 > U631 > tt > U423 > ok1
top > proper1 > U631 > tt > U433 > ok1
top > proper1 > U631 > tt > U452 > isNeList1 > ok1
top > proper1 > U631 > tt > U461 > ok1
top > proper1 > U631 > tt > U523 > ok1
top > proper1 > U631 > tt > U543 > ok1
top > proper1 > U631 > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > U631 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > U713 > isPalListKind1 > ok1
top > proper1 > U722 > isPal1 > isPalListKind1 > ok1
top > proper1 > U822 > isNePal1 > isPalListKind1 > ok1
top > proper1 > U831 > tt > U131 > ok1
top > proper1 > U831 > tt > U233 > ok1
top > proper1 > U831 > tt > U242 > U251 > ok1
top > proper1 > U831 > tt > isList1 > U213 > isPalListKind1 > ok1
top > proper1 > U831 > tt > isList1 > U213 > U223 > ok1
top > proper1 > U831 > tt > U322 > ok1
top > proper1 > U831 > tt > isQid1 > ok1
top > proper1 > U831 > tt > U423 > ok1
top > proper1 > U831 > tt > U433 > ok1
top > proper1 > U831 > tt > U452 > isNeList1 > ok1
top > proper1 > U831 > tt > U461 > ok1
top > proper1 > U831 > tt > U523 > ok1
top > proper1 > U831 > tt > U543 > ok1
top > proper1 > U831 > tt > isPal1 > isPalListKind1 > ok1
top > proper1 > U831 > tt > isNePal1 > isPalListKind1 > ok1
top > proper1 > a > ok1
top > proper1 > e
top > proper1 > i
top > proper1 > o > ok1
top > proper1 > u > ok1

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

(256) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(257) PisEmptyProof (EQUIVALENT transformation)

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

(258) TRUE

(259) Obligation:

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

U211(ok(X1), ok(X2), ok(X3)) → U211(X1, X2, X3)
U211(mark(X1), X2, X3) → U211(X1, X2, X3)

The TRS R consists of the following rules:

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

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

(260) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(mark(X1), X2, X3) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x1, x2, x3)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  x1
U31(x1, x2)  =  x1
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  U52(x1)
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  x1
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U21^13 > mark1
active1 > _2 > isQid > tt > U121 > mark1
active1 > _2 > isQid > tt > isPalListKind > U911 > mark1
active1 > _2 > isQid > tt > U521 > mark1
active1 > _2 > isQid > tt > U541 > mark1
active1 > _2 > isQid > tt > U561 > mark1
active1 > _2 > isQid > tt > U622 > mark1
active1 > _2 > isQid > tt > isPal1 > mark1
active1 > _2 > isQid > tt > U921 > mark1
active1 > U131 > tt > U121 > mark1
active1 > U131 > tt > isPalListKind > U911 > mark1
active1 > U131 > tt > U521 > mark1
active1 > U131 > tt > U541 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U622 > mark1
active1 > U131 > tt > isPal1 > mark1
active1 > U131 > tt > U921 > mark1
active1 > isNeList > isPalListKind > U911 > mark1
active1 > U221 > isPalListKind > U911 > mark1
active1 > U231 > isPalListKind > U911 > mark1
active1 > U241 > U251 > mark1
active1 > isList > tt > U121 > mark1
active1 > isList > tt > isPalListKind > U911 > mark1
active1 > isList > tt > U521 > mark1
active1 > isList > tt > U541 > mark1
active1 > isList > tt > U561 > mark1
active1 > isList > tt > U622 > mark1
active1 > isList > tt > isPal1 > mark1
active1 > isList > tt > U921 > mark1
active1 > U321 > mark1
active1 > U331 > tt > U121 > mark1
active1 > U331 > tt > isPalListKind > U911 > mark1
active1 > U331 > tt > U521 > mark1
active1 > U331 > tt > U541 > mark1
active1 > U331 > tt > U561 > mark1
active1 > U331 > tt > U622 > mark1
active1 > U331 > tt > isPal1 > mark1
active1 > U331 > tt > U921 > mark1
active1 > U421 > isPalListKind > U911 > mark1
active1 > U441 > mark1
active1 > U461 > tt > U121 > mark1
active1 > U461 > tt > isPalListKind > U911 > mark1
active1 > U461 > tt > U521 > mark1
active1 > U461 > tt > U541 > mark1
active1 > U461 > tt > U561 > mark1
active1 > U461 > tt > U622 > mark1
active1 > U461 > tt > isPal1 > mark1
active1 > U461 > tt > U921 > mark1
active1 > U531 > isPalListKind > U911 > mark1
active1 > U531 > U541 > mark1
active1 > U612 > isPalListKind > U911 > mark1
active1 > U612 > U622 > mark1
active1 > U631 > tt > U121 > mark1
active1 > U631 > tt > isPalListKind > U911 > mark1
active1 > U631 > tt > U521 > mark1
active1 > U631 > tt > U541 > mark1
active1 > U631 > tt > U561 > mark1
active1 > U631 > tt > U622 > mark1
active1 > U631 > tt > isPal1 > mark1
active1 > U631 > tt > U921 > mark1
active1 > U713 > U722 > U731 > isPalListKind > U911 > mark1
active1 > U713 > U722 > isPal1 > mark1
active1 > U812 > isPalListKind > U911 > mark1
active1 > U822 > mark1
proper1 > _2 > isQid > tt > U121 > mark1
proper1 > _2 > isQid > tt > isPalListKind > U911 > mark1
proper1 > _2 > isQid > tt > U521 > mark1
proper1 > _2 > isQid > tt > U541 > mark1
proper1 > _2 > isQid > tt > U561 > mark1
proper1 > _2 > isQid > tt > U622 > mark1
proper1 > _2 > isQid > tt > isPal1 > mark1
proper1 > _2 > isQid > tt > U921 > mark1
proper1 > nil > mark1
proper1 > U131 > tt > U121 > mark1
proper1 > U131 > tt > isPalListKind > U911 > mark1
proper1 > U131 > tt > U521 > mark1
proper1 > U131 > tt > U541 > mark1
proper1 > U131 > tt > U561 > mark1
proper1 > U131 > tt > U622 > mark1
proper1 > U131 > tt > isPal1 > mark1
proper1 > U131 > tt > U921 > mark1
proper1 > isNeList > isPalListKind > U911 > mark1
proper1 > U221 > isPalListKind > U911 > mark1
proper1 > U231 > isPalListKind > U911 > mark1
proper1 > U241 > U251 > mark1
proper1 > isList > tt > U121 > mark1
proper1 > isList > tt > isPalListKind > U911 > mark1
proper1 > isList > tt > U521 > mark1
proper1 > isList > tt > U541 > mark1
proper1 > isList > tt > U561 > mark1
proper1 > isList > tt > U622 > mark1
proper1 > isList > tt > isPal1 > mark1
proper1 > isList > tt > U921 > mark1
proper1 > U321 > mark1
proper1 > U331 > tt > U121 > mark1
proper1 > U331 > tt > isPalListKind > U911 > mark1
proper1 > U331 > tt > U521 > mark1
proper1 > U331 > tt > U541 > mark1
proper1 > U331 > tt > U561 > mark1
proper1 > U331 > tt > U622 > mark1
proper1 > U331 > tt > isPal1 > mark1
proper1 > U331 > tt > U921 > mark1
proper1 > U421 > isPalListKind > U911 > mark1
proper1 > U441 > mark1
proper1 > U461 > tt > U121 > mark1
proper1 > U461 > tt > isPalListKind > U911 > mark1
proper1 > U461 > tt > U521 > mark1
proper1 > U461 > tt > U541 > mark1
proper1 > U461 > tt > U561 > mark1
proper1 > U461 > tt > U622 > mark1
proper1 > U461 > tt > isPal1 > mark1
proper1 > U461 > tt > U921 > mark1
proper1 > U531 > isPalListKind > U911 > mark1
proper1 > U531 > U541 > mark1
proper1 > U612 > isPalListKind > U911 > mark1
proper1 > U612 > U622 > mark1
proper1 > U631 > tt > U121 > mark1
proper1 > U631 > tt > isPalListKind > U911 > mark1
proper1 > U631 > tt > U521 > mark1
proper1 > U631 > tt > U541 > mark1
proper1 > U631 > tt > U561 > mark1
proper1 > U631 > tt > U622 > mark1
proper1 > U631 > tt > isPal1 > mark1
proper1 > U631 > tt > U921 > mark1
proper1 > U713 > U722 > U731 > isPalListKind > U911 > mark1
proper1 > U713 > U722 > isPal1 > mark1
proper1 > U812 > isPalListKind > U911 > mark1
proper1 > U822 > mark1
proper1 > a > mark1
proper1 > e > mark1
proper1 > i > tt > U121 > mark1
proper1 > i > tt > isPalListKind > U911 > mark1
proper1 > i > tt > U521 > mark1
proper1 > i > tt > U541 > mark1
proper1 > i > tt > U561 > mark1
proper1 > i > tt > U622 > mark1
proper1 > i > tt > isPal1 > mark1
proper1 > i > tt > U921 > mark1
proper1 > o > mark1
proper1 > u > mark1
top > mark1

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

(261) Obligation:

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

U211(ok(X1), ok(X2), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(262) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U211(ok(X1), ok(X2), ok(X3)) → U211(X1, X2, X3)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U211(x1, x2, x3)  =  U211(x3)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  x3
U22(x1, x2, x3)  =  U22(x3)
U23(x1, x2, x3)  =  U23(x1, x3)
U24(x1, x2, x3)  =  U24(x1, x3)
U25(x1, x2)  =  x2
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(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)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U513 > ok1
active1 > U221 > U232 > isPalListKind1 > ok1
active1 > U221 > U232 > U242 > ok1
active1 > isList1 > tt > isNeList1 > U513 > ok1
active1 > isList1 > tt > U433 > isPalListKind1 > ok1
active1 > U312 > isPalListKind1 > ok1
active1 > U413 > isPalListKind1 > ok1
active1 > U422 > U433 > isPalListKind1 > ok1
active1 > U443 > U452 > isNeList1 > U513 > ok1
active1 > U612 > ok1
active1 > U732 > isPalListKind1 > ok1
active1 > U921 > tt > isNeList1 > U513 > ok1
active1 > U921 > tt > U433 > isPalListKind1 > ok1
proper1 > _2 > U513 > ok1
proper1 > nil
proper1 > U221 > U232 > isPalListKind1 > ok1
proper1 > U221 > U232 > U242 > ok1
proper1 > isList1 > tt > isNeList1 > U513 > ok1
proper1 > isList1 > tt > U433 > isPalListKind1 > ok1
proper1 > U312 > isPalListKind1 > ok1
proper1 > U413 > isPalListKind1 > ok1
proper1 > U422 > U433 > isPalListKind1 > ok1
proper1 > U443 > U452 > isNeList1 > U513 > ok1
proper1 > U612 > ok1
proper1 > U732 > isPalListKind1 > ok1
proper1 > U921 > tt > isNeList1 > U513 > ok1
proper1 > U921 > tt > U433 > isPalListKind1 > ok1
proper1 > a > tt > isNeList1 > U513 > ok1
proper1 > a > tt > U433 > isPalListKind1 > ok1
proper1 > e > tt > isNeList1 > U513 > ok1
proper1 > e > tt > U433 > isPalListKind1 > ok1
proper1 > i > ok1
proper1 > o > ok1
proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(263) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(264) PisEmptyProof (EQUIVALENT transformation)

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

(265) TRUE

(266) Obligation:

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

U131(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(267) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U131(mark(X)) → U131(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U131(x1)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > U112 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U223 > U233 > mark1
active1 > U131 > tt > U243 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > isQid > mark1
active1 > U131 > tt > U423 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U461 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U561 > mark1
active1 > U131 > tt > U722 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U213 > U223 > U233 > mark1
active1 > U312 > mark1
active1 > U413 > mark1
active1 > U443 > U452 > mark1
active1 > U513 > U523 > mark1
active1 > U533 > U543 > U552 > mark1
active1 > U612 > mark1
active1 > U713 > mark1
active1 > U812 > mark1
active1 > U822 > U831 > mark1
active1 > U912 > mark1
active1 > U921 > tt > U122 > mark1
active1 > U921 > tt > U223 > U233 > mark1
active1 > U921 > tt > U243 > mark1
active1 > U921 > tt > U252 > mark1
active1 > U921 > tt > isQid > mark1
active1 > U921 > tt > U423 > mark1
active1 > U921 > tt > U433 > mark1
active1 > U921 > tt > U452 > mark1
active1 > U921 > tt > U461 > mark1
active1 > U921 > tt > U523 > mark1
active1 > U921 > tt > U552 > mark1
active1 > U921 > tt > U561 > mark1
active1 > U921 > tt > U722 > mark1
active1 > U921 > tt > U732 > mark1
active1 > U921 > tt > U831 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > tt > U122 > mark1
o > tt > U223 > U233 > mark1
o > tt > U243 > mark1
o > tt > U252 > mark1
o > tt > isQid > mark1
o > tt > U423 > mark1
o > tt > U433 > mark1
o > tt > U452 > mark1
o > tt > U461 > mark1
o > tt > U523 > mark1
o > tt > U552 > mark1
o > tt > U561 > mark1
o > tt > U722 > mark1
o > tt > U732 > mark1
o > tt > U831 > mark1
u > mark1
top > mark1

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

(268) Obligation:

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

U131(ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(269) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U131(ok(X)) → U131(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U131(x1)  =  U131(x1)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  x2
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  x3
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  x2
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  U55(x2)
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  x1
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x2)
U82(x1, x2)  =  x2
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > tt > isNeList1 > ok1 > top
nil > tt > U421 > ok1 > top
nil > tt > U442 > ok1 > top
nil > tt > U451 > ok1 > top
nil > tt > U731 > ok1 > top
nil > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > _2 > ok1 > top
proper1 > isPal1 > U811 > active1 > U213 > ok1 > top
proper1 > isPal1 > U811 > active1 > U251 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isList1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U311 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > isQid1 > tt > isNePal1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U511 > ok1 > top
proper1 > isPal1 > U811 > active1 > U542 > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U551 > ok1 > top
proper1 > isPal1 > U811 > active1 > U912 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNeList1 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U421 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U442 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U451 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > U731 > ok1 > top
proper1 > isPal1 > U811 > active1 > U921 > tt > isNePal1 > ok1 > top
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > u > ok1 > top

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

(270) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(271) PisEmptyProof (EQUIVALENT transformation)

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

(272) TRUE

(273) Obligation:

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

U121(ok(X1), ok(X2)) → U121(X1, X2)
U121(mark(X1), X2) → U121(X1, X2)

The TRS R consists of the following rules:

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

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

(274) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U121(mark(X1), X2) → U121(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U121(x1, x2)  =  U121(x1, x2)
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
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)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1)
U82(x1, x2)  =  x1
U83(x1)  =  x1
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U513 > mark1
active1 > _2 > U513 > isPalListKind
active1 > U112 > U122 > mark1
active1 > U112 > isPalListKind
active1 > U213 > U223 > mark1
active1 > U213 > U223 > isPalListKind
active1 > U233 > mark1
active1 > U233 > isPalListKind
active1 > U243 > mark1
active1 > U252 > mark1
active1 > U312 > mark1
active1 > U312 > isPalListKind
active1 > U322 > mark1
active1 > U413 > U423 > mark1
active1 > U413 > U423 > isPalListKind
active1 > U433 > mark1
active1 > U433 > isPalListKind
active1 > U443 > U452 > mark1
active1 > U461 > mark1
active1 > U461 > tt > isPalListKind
active1 > U461 > tt > isPal
active1 > U523 > U533 > mark1
active1 > U523 > U533 > isPalListKind
active1 > U543 > U552 > mark1
active1 > U561 > mark1
active1 > U561 > tt > isPalListKind
active1 > U561 > tt > isPal
active1 > U711 > isPalListKind
active1 > U711 > U721 > mark1
active1 > U711 > U721 > isPal
active1 > U811 > mark1
active1 > U811 > isPalListKind
active1 > isNePal > isQid > mark1
active1 > isNePal > isQid > tt > isPalListKind
active1 > isNePal > isQid > tt > isPal
active1 > U911 > mark1
active1 > U911 > isPalListKind
proper1 > _2 > U513 > mark1
proper1 > _2 > U513 > isPalListKind
proper1 > nil
proper1 > U112 > U122 > mark1
proper1 > U112 > isPalListKind
proper1 > U213 > U223 > mark1
proper1 > U213 > U223 > isPalListKind
proper1 > U233 > mark1
proper1 > U233 > isPalListKind
proper1 > U243 > mark1
proper1 > U252 > mark1
proper1 > U312 > mark1
proper1 > U312 > isPalListKind
proper1 > U322 > mark1
proper1 > U413 > U423 > mark1
proper1 > U413 > U423 > isPalListKind
proper1 > U433 > mark1
proper1 > U433 > isPalListKind
proper1 > U443 > U452 > mark1
proper1 > U461 > mark1
proper1 > U461 > tt > isPalListKind
proper1 > U461 > tt > isPal
proper1 > U523 > U533 > mark1
proper1 > U523 > U533 > isPalListKind
proper1 > U543 > U552 > mark1
proper1 > U561 > mark1
proper1 > U561 > tt > isPalListKind
proper1 > U561 > tt > isPal
proper1 > U711 > isPalListKind
proper1 > U711 > U721 > mark1
proper1 > U711 > U721 > isPal
proper1 > U811 > mark1
proper1 > U811 > isPalListKind
proper1 > isNePal > isQid > mark1
proper1 > isNePal > isQid > tt > isPalListKind
proper1 > isNePal > isQid > tt > isPal
proper1 > U911 > mark1
proper1 > U911 > isPalListKind
proper1 > a
proper1 > e
proper1 > i
proper1 > o
proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(275) Obligation:

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

U121(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(276) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U121(ok(X1), ok(X2)) → U121(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U121(x1, x2)  =  x2
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  U11(x2)
tt  =  tt
U12(x1, x2)  =  U12(x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
U21(x1, x2, x3)  =  U21(x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  U23(x1, x3)
U24(x1, x2, x3)  =  U24(x1, x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x2)
U32(x1, x2)  =  U32(x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  x3
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x3)
U45(x1, x2)  =  U45(x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x3)
U52(x1, x2, x3)  =  x3
U53(x1, x2, x3)  =  x3
U54(x1, x2, x3)  =  x3
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  x2
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U713 > ok1
active1 > U111 > U121 > ok1
active1 > isPalListKind1 > tt > U121 > ok1
active1 > isPalListKind1 > tt > U232 > ok1
active1 > isPalListKind1 > tt > U242 > U251 > ok1
active1 > isPalListKind1 > tt > U242 > isList1 > ok1
active1 > isPalListKind1 > tt > U321 > ok1
active1 > isPalListKind1 > tt > U441 > ok1
active1 > isPalListKind1 > tt > U451 > ok1
active1 > isPalListKind1 > tt > U631 > ok1
active1 > isPalListKind1 > tt > U732 > ok1
active1 > isPalListKind1 > tt > U741 > ok1
active1 > isPalListKind1 > U912 > ok1
active1 > U131 > tt > U121 > ok1
active1 > U131 > tt > U232 > ok1
active1 > U131 > tt > U242 > U251 > ok1
active1 > U131 > tt > U242 > isList1 > ok1
active1 > U131 > tt > U321 > ok1
active1 > U131 > tt > U441 > ok1
active1 > U131 > tt > U451 > ok1
active1 > U131 > tt > U631 > ok1
active1 > U131 > tt > U732 > ok1
active1 > U131 > tt > U741 > ok1
active1 > U211 > ok1
active1 > U261 > tt > U121 > ok1
active1 > U261 > tt > U232 > ok1
active1 > U261 > tt > U242 > U251 > ok1
active1 > U261 > tt > U242 > isList1 > ok1
active1 > U261 > tt > U321 > ok1
active1 > U261 > tt > U441 > ok1
active1 > U261 > tt > U451 > ok1
active1 > U261 > tt > U631 > ok1
active1 > U261 > tt > U732 > ok1
active1 > U261 > tt > U741 > ok1
active1 > U311 > U321 > ok1
active1 > U331 > ok1
active1 > isQid1 > tt > U121 > ok1
active1 > isQid1 > tt > U232 > ok1
active1 > isQid1 > tt > U242 > U251 > ok1
active1 > isQid1 > tt > U242 > isList1 > ok1
active1 > isQid1 > tt > U321 > ok1
active1 > isQid1 > tt > U441 > ok1
active1 > isQid1 > tt > U451 > ok1
active1 > isQid1 > tt > U631 > ok1
active1 > isQid1 > tt > U732 > ok1
active1 > isQid1 > tt > U741 > ok1
active1 > U421 > ok1
active1 > U512 > ok1
active1 > U612 > ok1
active1 > U622 > U631 > ok1
active1 > U812 > ok1
active1 > U831 > tt > U121 > ok1
active1 > U831 > tt > U232 > ok1
active1 > U831 > tt > U242 > U251 > ok1
active1 > U831 > tt > U242 > isList1 > ok1
active1 > U831 > tt > U321 > ok1
active1 > U831 > tt > U441 > ok1
active1 > U831 > tt > U451 > ok1
active1 > U831 > tt > U631 > ok1
active1 > U831 > tt > U732 > ok1
active1 > U831 > tt > U741 > ok1
proper1 > _2 > U713 > ok1
proper1 > nil > ok1
proper1 > U111 > U121 > ok1
proper1 > isPalListKind1 > tt > U121 > ok1
proper1 > isPalListKind1 > tt > U232 > ok1
proper1 > isPalListKind1 > tt > U242 > U251 > ok1
proper1 > isPalListKind1 > tt > U242 > isList1 > ok1
proper1 > isPalListKind1 > tt > U321 > ok1
proper1 > isPalListKind1 > tt > U441 > ok1
proper1 > isPalListKind1 > tt > U451 > ok1
proper1 > isPalListKind1 > tt > U631 > ok1
proper1 > isPalListKind1 > tt > U732 > ok1
proper1 > isPalListKind1 > tt > U741 > ok1
proper1 > isPalListKind1 > U912 > ok1
proper1 > U131 > tt > U121 > ok1
proper1 > U131 > tt > U232 > ok1
proper1 > U131 > tt > U242 > U251 > ok1
proper1 > U131 > tt > U242 > isList1 > ok1
proper1 > U131 > tt > U321 > ok1
proper1 > U131 > tt > U441 > ok1
proper1 > U131 > tt > U451 > ok1
proper1 > U131 > tt > U631 > ok1
proper1 > U131 > tt > U732 > ok1
proper1 > U131 > tt > U741 > ok1
proper1 > U211 > ok1
proper1 > U261 > tt > U121 > ok1
proper1 > U261 > tt > U232 > ok1
proper1 > U261 > tt > U242 > U251 > ok1
proper1 > U261 > tt > U242 > isList1 > ok1
proper1 > U261 > tt > U321 > ok1
proper1 > U261 > tt > U441 > ok1
proper1 > U261 > tt > U451 > ok1
proper1 > U261 > tt > U631 > ok1
proper1 > U261 > tt > U732 > ok1
proper1 > U261 > tt > U741 > ok1
proper1 > U311 > U321 > ok1
proper1 > U331 > ok1
proper1 > isQid1 > tt > U121 > ok1
proper1 > isQid1 > tt > U232 > ok1
proper1 > isQid1 > tt > U242 > U251 > ok1
proper1 > isQid1 > tt > U242 > isList1 > ok1
proper1 > isQid1 > tt > U321 > ok1
proper1 > isQid1 > tt > U441 > ok1
proper1 > isQid1 > tt > U451 > ok1
proper1 > isQid1 > tt > U631 > ok1
proper1 > isQid1 > tt > U732 > ok1
proper1 > isQid1 > tt > U741 > ok1
proper1 > U421 > ok1
proper1 > U512 > ok1
proper1 > U612 > ok1
proper1 > U622 > U631 > ok1
proper1 > U812 > ok1
proper1 > U831 > tt > U121 > ok1
proper1 > U831 > tt > U232 > ok1
proper1 > U831 > tt > U242 > U251 > ok1
proper1 > U831 > tt > U242 > isList1 > ok1
proper1 > U831 > tt > U321 > ok1
proper1 > U831 > tt > U441 > ok1
proper1 > U831 > tt > U451 > ok1
proper1 > U831 > tt > U631 > ok1
proper1 > U831 > tt > U732 > ok1
proper1 > U831 > tt > U741 > ok1
proper1 > a
proper1 > e > ok1
proper1 > i > ok1
proper1 > o > ok1
proper1 > u > ok1

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

(277) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(278) PisEmptyProof (EQUIVALENT transformation)

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

(279) TRUE

(280) Obligation:

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

U111(ok(X1), ok(X2)) → U111(X1, X2)
U111(mark(X1), X2) → U111(X1, X2)

The TRS R consists of the following rules:

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

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

(281) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U111(mark(X1), X2) → U111(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U111(x1, x2)  =  x1
ok(x1)  =  x1
mark(x1)  =  mark(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  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, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > tt > U122 > mark1
active1 > tt > U252 > isList1 > U112 > mark1
active1 > tt > U252 > isList1 > U213 > U223 > U233 > U243 > mark1
active1 > tt > U252 > U261 > mark1
active1 > tt > U322 > mark1
active1 > tt > U331 > mark1
active1 > tt > U423 > U433 > mark1
active1 > tt > U443 > mark1
active1 > tt > U452 > U461 > mark1
active1 > tt > U523 > mark1
active1 > tt > U533 > U543 > mark1
active1 > tt > U552 > U561 > mark1
active1 > tt > U622 > mark1
active1 > tt > U722 > mark1
active1 > tt > U822 > U831 > mark1
active1 > tt > U921 > mark1
active1 > isPalListKind > proper1 > _2 > U213 > U223 > U233 > U243 > mark1
active1 > isPalListKind > proper1 > _2 > U513 > U523 > mark1
active1 > isPalListKind > proper1 > nil > mark1
active1 > isPalListKind > proper1 > U122 > mark1
active1 > isPalListKind > proper1 > U252 > isList1 > U112 > mark1
active1 > isPalListKind > proper1 > U252 > isList1 > U213 > U223 > U233 > U243 > mark1
active1 > isPalListKind > proper1 > U252 > U261 > mark1
active1 > isPalListKind > proper1 > U312 > U322 > mark1
active1 > isPalListKind > proper1 > U331 > mark1
active1 > isPalListKind > proper1 > U413 > U423 > U433 > mark1
active1 > isPalListKind > proper1 > U443 > mark1
active1 > isPalListKind > proper1 > U452 > U461 > mark1
active1 > isPalListKind > proper1 > U533 > U543 > mark1
active1 > isPalListKind > proper1 > U552 > U561 > mark1
active1 > isPalListKind > proper1 > U612 > U622 > mark1
active1 > isPalListKind > proper1 > U713 > U722 > mark1
active1 > isPalListKind > proper1 > U812 > U822 > U831 > mark1
active1 > isPalListKind > proper1 > U911 > U921 > mark1
active1 > isPalListKind > proper1 > a > mark1
active1 > isPalListKind > proper1 > e > mark1
active1 > isPalListKind > proper1 > o > mark1
active1 > isPalListKind > proper1 > u > mark1
i > tt > U122 > mark1
i > tt > U252 > isList1 > U112 > mark1
i > tt > U252 > isList1 > U213 > U223 > U233 > U243 > mark1
i > tt > U252 > U261 > mark1
i > tt > U322 > mark1
i > tt > U331 > mark1
i > tt > U423 > U433 > mark1
i > tt > U443 > mark1
i > tt > U452 > U461 > mark1
i > tt > U523 > mark1
i > tt > U533 > U543 > mark1
i > tt > U552 > U561 > mark1
i > tt > U622 > mark1
i > tt > U722 > mark1
i > tt > U822 > U831 > mark1
i > tt > U921 > mark1

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

(282) Obligation:

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

U111(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(283) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


U111(ok(X1), ok(X2)) → U111(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
U111(x1, x2)  =  U111(x1, x2)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  x2
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x2, x3)
U23(x1, x2, x3)  =  U23(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)  =  x2
U32(x1, x2)  =  x2
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x3)
U42(x1, x2, x3)  =  x3
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  U44(x1, x3)
U45(x1, x2)  =  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(x2, x3)
U55(x1, x2)  =  x2
U56(x1)  =  x1
U61(x1, x2)  =  x2
U62(x1, x2)  =  x2
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  x3
U72(x1, x2)  =  x2
U73(x1, x2)  =  x2
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x2
U82(x1, x2)  =  x2
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
U11^12 > ok1
proper1 > _2 > ok1
proper1 > nil > tt > U122 > ok1
proper1 > nil > tt > U131 > ok1
proper1 > nil > tt > isNeList1 > U412 > ok1
proper1 > nil > tt > U232 > ok1
proper1 > nil > tt > U243 > U252 > ok1
proper1 > nil > tt > U243 > isList1 > ok1
proper1 > nil > tt > U261 > ok1
proper1 > nil > tt > U442 > isList1 > ok1
proper1 > nil > tt > U523 > ok1
proper1 > nil > tt > U631 > ok1
proper1 > nil > tt > isPal1 > ok1
proper1 > nil > tt > U831 > ok1
proper1 > U213 > ok1
proper1 > U222 > U232 > ok1
proper1 > U331 > tt > U122 > ok1
proper1 > U331 > tt > U131 > ok1
proper1 > U331 > tt > isNeList1 > U412 > ok1
proper1 > U331 > tt > U232 > ok1
proper1 > U331 > tt > U243 > U252 > ok1
proper1 > U331 > tt > U243 > isList1 > ok1
proper1 > U331 > tt > U261 > ok1
proper1 > U331 > tt > U442 > isList1 > ok1
proper1 > U331 > tt > U523 > ok1
proper1 > U331 > tt > U631 > ok1
proper1 > U331 > tt > isPal1 > ok1
proper1 > U331 > tt > U831 > ok1
proper1 > U513 > ok1
proper1 > U533 > ok1
proper1 > U542 > isNeList1 > U412 > ok1
proper1 > U741 > tt > U122 > ok1
proper1 > U741 > tt > U131 > ok1
proper1 > U741 > tt > isNeList1 > U412 > ok1
proper1 > U741 > tt > U232 > ok1
proper1 > U741 > tt > U243 > U252 > ok1
proper1 > U741 > tt > U243 > isList1 > ok1
proper1 > U741 > tt > U261 > ok1
proper1 > U741 > tt > U442 > isList1 > ok1
proper1 > U741 > tt > U523 > ok1
proper1 > U741 > tt > U631 > ok1
proper1 > U741 > tt > isPal1 > ok1
proper1 > U741 > tt > U831 > ok1
proper1 > a > ok1
proper1 > e > tt > U122 > ok1
proper1 > e > tt > U131 > ok1
proper1 > e > tt > isNeList1 > U412 > ok1
proper1 > e > tt > U232 > ok1
proper1 > e > tt > U243 > U252 > ok1
proper1 > e > tt > U243 > isList1 > ok1
proper1 > e > tt > U261 > ok1
proper1 > e > tt > U442 > isList1 > ok1
proper1 > e > tt > U523 > ok1
proper1 > e > tt > U631 > ok1
proper1 > e > tt > isPal1 > ok1
proper1 > e > tt > U831 > ok1
proper1 > i > ok1
proper1 > o > ok1
proper1 > u > ok1
top > active1 > _2 > ok1
top > active1 > U213 > ok1
top > active1 > U222 > U232 > ok1
top > active1 > U331 > tt > U122 > ok1
top > active1 > U331 > tt > U131 > ok1
top > active1 > U331 > tt > isNeList1 > U412 > ok1
top > active1 > U331 > tt > U232 > ok1
top > active1 > U331 > tt > U243 > U252 > ok1
top > active1 > U331 > tt > U243 > isList1 > ok1
top > active1 > U331 > tt > U261 > ok1
top > active1 > U331 > tt > U442 > isList1 > ok1
top > active1 > U331 > tt > U523 > ok1
top > active1 > U331 > tt > U631 > ok1
top > active1 > U331 > tt > isPal1 > ok1
top > active1 > U331 > tt > U831 > ok1
top > active1 > U513 > ok1
top > active1 > U533 > ok1
top > active1 > U542 > isNeList1 > U412 > ok1
top > active1 > U741 > tt > U122 > ok1
top > active1 > U741 > tt > U131 > ok1
top > active1 > U741 > tt > isNeList1 > U412 > ok1
top > active1 > U741 > tt > U232 > ok1
top > active1 > U741 > tt > U243 > U252 > ok1
top > active1 > U741 > tt > U243 > isList1 > ok1
top > active1 > U741 > tt > U261 > ok1
top > active1 > U741 > tt > U442 > isList1 > ok1
top > active1 > U741 > tt > U523 > ok1
top > active1 > U741 > tt > U631 > ok1
top > active1 > U741 > tt > isPal1 > ok1
top > active1 > U741 > tt > U831 > ok1

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

(284) Obligation:

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

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

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

(285) PisEmptyProof (EQUIVALENT transformation)

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

(286) TRUE

(287) Obligation:

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

__1(X1, mark(X2)) → __1(X1, X2)
__1(mark(X1), X2) → __1(X1, X2)
__1(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(288) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(mark(X1), X2) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  x1
mark(x1)  =  mark(x1)
ok(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1)
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  U52(x1)
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  U55(x1)
U56(x1)  =  U56(x1)
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1)
U72(x1, x2)  =  x1
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  x1
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
top > active1 > _2 > isPalListKind > mark1
top > active1 > _2 > isPalListKind > tt
top > active1 > _2 > isQid > mark1
top > active1 > _2 > isQid > tt
top > active1 > _2 > U511 > U521 > mark1
top > active1 > _2 > U711 > mark1
top > active1 > U111 > mark1
top > active1 > U131 > mark1
top > active1 > U131 > tt
top > active1 > U221 > mark1
top > active1 > U241 > isList > mark1
top > active1 > U241 > isList > tt
top > active1 > U261 > mark1
top > active1 > U261 > tt
top > active1 > U311 > isPalListKind > mark1
top > active1 > U311 > isPalListKind > tt
top > active1 > U331 > mark1
top > active1 > U331 > tt
top > active1 > U421 > U431 > isPalListKind > mark1
top > active1 > U421 > U431 > isPalListKind > tt
top > active1 > U451 > isNeList > mark1
top > active1 > U551 > isList > mark1
top > active1 > U551 > isList > tt
top > active1 > U551 > U561 > mark1
top > active1 > U551 > U561 > tt
top > active1 > U731 > mark1
top > active1 > isPal > tt
top > active1 > U741 > mark1
top > active1 > U741 > tt
top > active1 > isNePal > isPalListKind > mark1
top > active1 > isNePal > isPalListKind > tt
top > active1 > isNePal > U711 > mark1
top > active1 > U911 > isPalListKind > mark1
top > active1 > U911 > isPalListKind > tt
top > proper1 > _2 > isPalListKind > mark1
top > proper1 > _2 > isPalListKind > tt
top > proper1 > _2 > isQid > mark1
top > proper1 > _2 > isQid > tt
top > proper1 > _2 > U511 > U521 > mark1
top > proper1 > _2 > U711 > mark1
top > proper1 > nil > mark1
top > proper1 > nil > tt
top > proper1 > U111 > mark1
top > proper1 > U131 > mark1
top > proper1 > U131 > tt
top > proper1 > U221 > mark1
top > proper1 > U241 > isList > mark1
top > proper1 > U241 > isList > tt
top > proper1 > U261 > mark1
top > proper1 > U261 > tt
top > proper1 > U311 > isPalListKind > mark1
top > proper1 > U311 > isPalListKind > tt
top > proper1 > U331 > mark1
top > proper1 > U331 > tt
top > proper1 > U421 > U431 > isPalListKind > mark1
top > proper1 > U421 > U431 > isPalListKind > tt
top > proper1 > U451 > isNeList > mark1
top > proper1 > U551 > isList > mark1
top > proper1 > U551 > isList > tt
top > proper1 > U551 > U561 > mark1
top > proper1 > U551 > U561 > tt
top > proper1 > U731 > mark1
top > proper1 > isPal > tt
top > proper1 > U741 > mark1
top > proper1 > U741 > tt
top > proper1 > isNePal > isPalListKind > mark1
top > proper1 > isNePal > isPalListKind > tt
top > proper1 > isNePal > U711 > mark1
top > proper1 > U911 > isPalListKind > mark1
top > proper1 > U911 > isPalListKind > tt
top > proper1 > a > mark1
top > proper1 > a > tt
top > proper1 > e > mark1
top > proper1 > e > tt
top > proper1 > i > mark1
top > proper1 > i > tt
top > proper1 > o
top > proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(289) Obligation:

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

__1(X1, mark(X2)) → __1(X1, X2)
__1(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(290) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(X1, mark(X2)) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  __1(x1, x2)
mark(x1)  =  mark(x1)
ok(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  x1
U22(x1, x2, x3)  =  U22(x1)
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  x1
isList(x1)  =  isList
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  x1
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  x1
U56(x1)  =  x1
U61(x1, x2)  =  x1
U62(x1, x2)  =  x1
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x1, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
_^12 > mark1
proper1 > _2 > mark1
proper1 > nil > mark1
proper1 > U121 > mark1
proper1 > U221 > isPalListKind > mark1
proper1 > isList > mark1
proper1 > U261 > tt > U241 > mark1
proper1 > U261 > tt > U421 > mark1
proper1 > U311 > isPalListKind > mark1
proper1 > isQid > tt > U241 > mark1
proper1 > isQid > tt > U421 > mark1
proper1 > U411 > isPalListKind > mark1
proper1 > U411 > U421 > mark1
proper1 > U431 > mark1
proper1 > U451 > isNeList > isPalListKind > mark1
proper1 > U461 > tt > U241 > mark1
proper1 > U461 > tt > U421 > mark1
proper1 > U511 > isPalListKind > mark1
proper1 > U531 > isPalListKind > mark1
proper1 > U541 > mark1
proper1 > U631 > tt > U241 > mark1
proper1 > U631 > tt > U421 > mark1
proper1 > U712 > isPalListKind > mark1
proper1 > U712 > U722 > mark1
proper1 > U741 > tt > U241 > mark1
proper1 > U741 > tt > U421 > mark1
proper1 > U812 > isPalListKind > mark1
proper1 > U822 > U831 > tt > U241 > mark1
proper1 > U822 > U831 > tt > U421 > mark1
proper1 > U921 > tt > U241 > mark1
proper1 > U921 > tt > U421 > mark1
proper1 > a > tt > U241 > mark1
proper1 > a > tt > U421 > mark1
proper1 > e > mark1
proper1 > i > mark1
proper1 > o > mark1
proper1 > u > mark1
top > active1 > _2 > mark1
top > active1 > U121 > mark1
top > active1 > U221 > isPalListKind > mark1
top > active1 > isList > mark1
top > active1 > U261 > tt > U241 > mark1
top > active1 > U261 > tt > U421 > mark1
top > active1 > U311 > isPalListKind > mark1
top > active1 > isQid > tt > U241 > mark1
top > active1 > isQid > tt > U421 > mark1
top > active1 > U411 > isPalListKind > mark1
top > active1 > U411 > U421 > mark1
top > active1 > U431 > mark1
top > active1 > U451 > isNeList > isPalListKind > mark1
top > active1 > U461 > tt > U241 > mark1
top > active1 > U461 > tt > U421 > mark1
top > active1 > U511 > isPalListKind > mark1
top > active1 > U531 > isPalListKind > mark1
top > active1 > U541 > mark1
top > active1 > U631 > tt > U241 > mark1
top > active1 > U631 > tt > U421 > mark1
top > active1 > U712 > isPalListKind > mark1
top > active1 > U712 > U722 > mark1
top > active1 > U741 > tt > U241 > mark1
top > active1 > U741 > tt > U421 > mark1
top > active1 > U812 > isPalListKind > mark1
top > active1 > U822 > U831 > tt > U241 > mark1
top > active1 > U822 > U831 > tt > U421 > mark1
top > active1 > U921 > tt > U241 > mark1
top > active1 > U921 > tt > U421 > mark1

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

(291) Obligation:

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

__1(ok(X1), ok(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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(292) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


__1(ok(X1), ok(X2)) → __1(X1, X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
__1(x1, x2)  =  __1(x1, x2)
ok(x1)  =  ok(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  x3
U23(x1, x2, x3)  =  x3
U24(x1, x2, x3)  =  U24(x1, x3)
U25(x1, x2)  =  U25(x2)
isList(x1)  =  isList(x1)
U26(x1)  =  U26(x1)
U31(x1, x2)  =  x2
U32(x1, x2)  =  x2
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x3)
U43(x1, x2, x3)  =  x3
U44(x1, x2, x3)  =  x3
U45(x1, x2)  =  U45(x2)
U46(x1)  =  U46(x1)
U51(x1, x2, x3)  =  U51(x2, x3)
U52(x1, x2, x3)  =  U52(x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x3)
U55(x1, x2)  =  x2
U56(x1)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x2)
U63(x1)  =  U63(x1)
U71(x1, x2, x3)  =  U71(x2, x3)
U72(x1, x2)  =  U72(x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  U83(x1)
isNePal(x1)  =  x1
U91(x1, x2)  =  x2
U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > U213 > ok1
active1 > _2 > U512 > U522 > ok1
active1 > _2 > U712 > U721 > ok1
active1 > U112 > U122 > ok1
active1 > U261 > tt > U122 > ok1
active1 > U261 > tt > U131 > ok1
active1 > U261 > tt > isNeList1 > U512 > U522 > ok1
active1 > U261 > tt > U242 > ok1
active1 > U261 > tt > U251 > isList1 > U213 > ok1
active1 > U261 > tt > U421 > ok1
active1 > U261 > tt > U451 > U461 > ok1
active1 > U261 > tt > U533 > U542 > ok1
active1 > U261 > tt > U561 > ok1
active1 > U261 > tt > U621 > U631 > ok1
active1 > U261 > tt > U721 > ok1
active1 > U261 > tt > U732 > ok1
active1 > U261 > tt > isPal1 > ok1
active1 > U261 > tt > U741 > ok1
active1 > U331 > tt > U122 > ok1
active1 > U331 > tt > U131 > ok1
active1 > U331 > tt > isNeList1 > U512 > U522 > ok1
active1 > U331 > tt > U242 > ok1
active1 > U331 > tt > U251 > isList1 > U213 > ok1
active1 > U331 > tt > U421 > ok1
active1 > U331 > tt > U451 > U461 > ok1
active1 > U331 > tt > U533 > U542 > ok1
active1 > U331 > tt > U561 > ok1
active1 > U331 > tt > U621 > U631 > ok1
active1 > U331 > tt > U721 > ok1
active1 > U331 > tt > U732 > ok1
active1 > U331 > tt > isPal1 > ok1
active1 > U331 > tt > U741 > ok1
active1 > U413 > U421 > ok1
active1 > U612 > ok1
active1 > U812 > ok1
active1 > U822 > U831 > tt > U122 > ok1
active1 > U822 > U831 > tt > U131 > ok1
active1 > U822 > U831 > tt > isNeList1 > U512 > U522 > ok1
active1 > U822 > U831 > tt > U242 > ok1
active1 > U822 > U831 > tt > U251 > isList1 > U213 > ok1
active1 > U822 > U831 > tt > U421 > ok1
active1 > U822 > U831 > tt > U451 > U461 > ok1
active1 > U822 > U831 > tt > U533 > U542 > ok1
active1 > U822 > U831 > tt > U561 > ok1
active1 > U822 > U831 > tt > U621 > U631 > ok1
active1 > U822 > U831 > tt > U721 > ok1
active1 > U822 > U831 > tt > U732 > ok1
active1 > U822 > U831 > tt > isPal1 > ok1
active1 > U822 > U831 > tt > U741 > ok1
nil > tt > U122 > ok1
nil > tt > U131 > ok1
nil > tt > isNeList1 > U512 > U522 > ok1
nil > tt > U242 > ok1
nil > tt > U251 > isList1 > U213 > ok1
nil > tt > U421 > ok1
nil > tt > U451 > U461 > ok1
nil > tt > U533 > U542 > ok1
nil > tt > U561 > ok1
nil > tt > U621 > U631 > ok1
nil > tt > U721 > ok1
nil > tt > U732 > ok1
nil > tt > isPal1 > ok1
nil > tt > U741 > ok1
proper1 > _2 > U213 > ok1
proper1 > _2 > U512 > U522 > ok1
proper1 > _2 > U712 > U721 > ok1
proper1 > U112 > U122 > ok1
proper1 > U261 > tt > U122 > ok1
proper1 > U261 > tt > U131 > ok1
proper1 > U261 > tt > isNeList1 > U512 > U522 > ok1
proper1 > U261 > tt > U242 > ok1
proper1 > U261 > tt > U251 > isList1 > U213 > ok1
proper1 > U261 > tt > U421 > ok1
proper1 > U261 > tt > U451 > U461 > ok1
proper1 > U261 > tt > U533 > U542 > ok1
proper1 > U261 > tt > U561 > ok1
proper1 > U261 > tt > U621 > U631 > ok1
proper1 > U261 > tt > U721 > ok1
proper1 > U261 > tt > U732 > ok1
proper1 > U261 > tt > isPal1 > ok1
proper1 > U261 > tt > U741 > ok1
proper1 > U331 > tt > U122 > ok1
proper1 > U331 > tt > U131 > ok1
proper1 > U331 > tt > isNeList1 > U512 > U522 > ok1
proper1 > U331 > tt > U242 > ok1
proper1 > U331 > tt > U251 > isList1 > U213 > ok1
proper1 > U331 > tt > U421 > ok1
proper1 > U331 > tt > U451 > U461 > ok1
proper1 > U331 > tt > U533 > U542 > ok1
proper1 > U331 > tt > U561 > ok1
proper1 > U331 > tt > U621 > U631 > ok1
proper1 > U331 > tt > U721 > ok1
proper1 > U331 > tt > U732 > ok1
proper1 > U331 > tt > isPal1 > ok1
proper1 > U331 > tt > U741 > ok1
proper1 > U413 > U421 > ok1
proper1 > U612 > ok1
proper1 > U812 > ok1
proper1 > U822 > U831 > tt > U122 > ok1
proper1 > U822 > U831 > tt > U131 > ok1
proper1 > U822 > U831 > tt > isNeList1 > U512 > U522 > ok1
proper1 > U822 > U831 > tt > U242 > ok1
proper1 > U822 > U831 > tt > U251 > isList1 > U213 > ok1
proper1 > U822 > U831 > tt > U421 > ok1
proper1 > U822 > U831 > tt > U451 > U461 > ok1
proper1 > U822 > U831 > tt > U533 > U542 > ok1
proper1 > U822 > U831 > tt > U561 > ok1
proper1 > U822 > U831 > tt > U621 > U631 > ok1
proper1 > U822 > U831 > tt > U721 > ok1
proper1 > U822 > U831 > tt > U732 > ok1
proper1 > U822 > U831 > tt > isPal1 > ok1
proper1 > U822 > U831 > tt > U741 > ok1
proper1 > a
proper1 > e > ok1
proper1 > i > ok1
proper1 > o
proper1 > u > ok1

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

(293) Obligation:

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

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

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

(294) PisEmptyProof (EQUIVALENT transformation)

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

(295) TRUE

(296) Obligation:

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

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

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

(297) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


PROPER(__(X1, X2)) → PROPER(X2)
PROPER(__(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X1)
PROPER(U11(X1, X2)) → PROPER(X2)
PROPER(U12(X1, X2)) → PROPER(X1)
PROPER(U12(X1, X2)) → PROPER(X2)
PROPER(isPalListKind(X)) → PROPER(X)
PROPER(U21(X1, X2, X3)) → PROPER(X1)
PROPER(U21(X1, X2, X3)) → PROPER(X2)
PROPER(U21(X1, X2, X3)) → PROPER(X3)
PROPER(U22(X1, X2, X3)) → PROPER(X1)
PROPER(U22(X1, X2, X3)) → PROPER(X2)
PROPER(U22(X1, X2, X3)) → PROPER(X3)
PROPER(U23(X1, X2, X3)) → PROPER(X1)
PROPER(U23(X1, X2, X3)) → PROPER(X2)
PROPER(U23(X1, X2, X3)) → PROPER(X3)
PROPER(U24(X1, X2, X3)) → PROPER(X1)
PROPER(U24(X1, X2, X3)) → PROPER(X2)
PROPER(U24(X1, X2, X3)) → PROPER(X3)
PROPER(U25(X1, X2)) → PROPER(X1)
PROPER(U25(X1, X2)) → PROPER(X2)
PROPER(U31(X1, X2)) → PROPER(X1)
PROPER(U31(X1, X2)) → PROPER(X2)
PROPER(U32(X1, X2)) → PROPER(X1)
PROPER(U32(X1, X2)) → PROPER(X2)
PROPER(U41(X1, X2, X3)) → PROPER(X1)
PROPER(U41(X1, X2, X3)) → PROPER(X2)
PROPER(U41(X1, X2, X3)) → PROPER(X3)
PROPER(U42(X1, X2, X3)) → PROPER(X1)
PROPER(U42(X1, X2, X3)) → PROPER(X2)
PROPER(U42(X1, X2, X3)) → PROPER(X3)
PROPER(U43(X1, X2, X3)) → PROPER(X1)
PROPER(U43(X1, X2, X3)) → PROPER(X2)
PROPER(U43(X1, X2, X3)) → PROPER(X3)
PROPER(U44(X1, X2, X3)) → PROPER(X1)
PROPER(U44(X1, X2, X3)) → PROPER(X2)
PROPER(U44(X1, X2, X3)) → PROPER(X3)
PROPER(U45(X1, X2)) → PROPER(X1)
PROPER(U45(X1, X2)) → PROPER(X2)
PROPER(U51(X1, X2, X3)) → PROPER(X1)
PROPER(U51(X1, X2, X3)) → PROPER(X2)
PROPER(U51(X1, X2, X3)) → PROPER(X3)
PROPER(U52(X1, X2, X3)) → PROPER(X1)
PROPER(U52(X1, X2, X3)) → PROPER(X2)
PROPER(U52(X1, X2, X3)) → PROPER(X3)
PROPER(U53(X1, X2, X3)) → PROPER(X1)
PROPER(U53(X1, X2, X3)) → PROPER(X2)
PROPER(U53(X1, X2, X3)) → PROPER(X3)
PROPER(U54(X1, X2, X3)) → PROPER(X1)
PROPER(U54(X1, X2, X3)) → PROPER(X2)
PROPER(U54(X1, X2, X3)) → PROPER(X3)
PROPER(U55(X1, X2)) → PROPER(X1)
PROPER(U55(X1, X2)) → PROPER(X2)
PROPER(U61(X1, X2)) → PROPER(X1)
PROPER(U61(X1, X2)) → PROPER(X2)
PROPER(U62(X1, X2)) → PROPER(X1)
PROPER(U62(X1, X2)) → PROPER(X2)
PROPER(U71(X1, X2, X3)) → PROPER(X1)
PROPER(U71(X1, X2, X3)) → PROPER(X2)
PROPER(U71(X1, X2, X3)) → PROPER(X3)
PROPER(U72(X1, X2)) → PROPER(X1)
PROPER(U72(X1, X2)) → PROPER(X2)
PROPER(U73(X1, X2)) → PROPER(X1)
PROPER(U73(X1, X2)) → PROPER(X2)
PROPER(U81(X1, X2)) → PROPER(X1)
PROPER(U81(X1, X2)) → PROPER(X2)
PROPER(U82(X1, X2)) → PROPER(X1)
PROPER(U82(X1, X2)) → PROPER(X2)
PROPER(U91(X1, X2)) → PROPER(X1)
PROPER(U91(X1, X2)) → PROPER(X2)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
PROPER(x1)  =  PROPER(x1)
__(x1, x2)  =  __(x1, x2)
U11(x1, x2)  =  U11(x1, x2)
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(x1)
U13(x1)  =  x1
isNeList(x1)  =  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)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  x1
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  x1
nil  =  nil
tt  =  tt
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > ok > U112
nil > ok > U252
nil > ok > U533
nil > ok > U612
nil > ok > U732
a > ok > U112
a > ok > U252
a > ok > U533
a > ok > U612
a > ok > U732
e > ok > U112
e > ok > U252
e > ok > U533
e > ok > U612
e > ok > U732
i > ok > U112
i > ok > U252
i > ok > U533
i > ok > U612
i > ok > U732
o > ok > U112
o > ok > U252
o > ok > U533
o > ok > U612
o > ok > U732
u > ok > U112
u > ok > U252
u > ok > U533
u > ok > U612
u > ok > U732
top > active1 > _2 > isPalListKind1 > ok > U112
top > active1 > _2 > isPalListKind1 > ok > U252
top > active1 > _2 > isPalListKind1 > ok > U533
top > active1 > _2 > isPalListKind1 > ok > U612
top > active1 > _2 > isPalListKind1 > ok > U732
top > active1 > _2 > U713 > ok > U112
top > active1 > _2 > U713 > ok > U252
top > active1 > _2 > U713 > ok > U533
top > active1 > _2 > U713 > ok > U612
top > active1 > _2 > U713 > ok > U732
top > active1 > U122 > ok > U112
top > active1 > U122 > ok > U252
top > active1 > U122 > ok > U533
top > active1 > U122 > ok > U612
top > active1 > U122 > ok > U732
top > active1 > U213 > U223 > isPalListKind1 > ok > U112
top > active1 > U213 > U223 > isPalListKind1 > ok > U252
top > active1 > U213 > U223 > isPalListKind1 > ok > U533
top > active1 > U213 > U223 > isPalListKind1 > ok > U612
top > active1 > U213 > U223 > isPalListKind1 > ok > U732
top > active1 > U233 > isPalListKind1 > ok > U112
top > active1 > U233 > isPalListKind1 > ok > U252
top > active1 > U233 > isPalListKind1 > ok > U533
top > active1 > U233 > isPalListKind1 > ok > U612
top > active1 > U233 > isPalListKind1 > ok > U732
top > active1 > U233 > U243 > U252
top > active1 > U312 > isPalListKind1 > ok > U112
top > active1 > U312 > isPalListKind1 > ok > U252
top > active1 > U312 > isPalListKind1 > ok > U533
top > active1 > U312 > isPalListKind1 > ok > U612
top > active1 > U312 > isPalListKind1 > ok > U732
top > active1 > U312 > U322
top > active1 > U413 > isPalListKind1 > ok > U112
top > active1 > U413 > isPalListKind1 > ok > U252
top > active1 > U413 > isPalListKind1 > ok > U533
top > active1 > U413 > isPalListKind1 > ok > U612
top > active1 > U413 > isPalListKind1 > ok > U732
top > active1 > U423 > isPalListKind1 > ok > U112
top > active1 > U423 > isPalListKind1 > ok > U252
top > active1 > U423 > isPalListKind1 > ok > U533
top > active1 > U423 > isPalListKind1 > ok > U612
top > active1 > U423 > isPalListKind1 > ok > U732
top > active1 > U423 > U433
top > active1 > U443 > U452 > ok > U112
top > active1 > U443 > U452 > ok > U252
top > active1 > U443 > U452 > ok > U533
top > active1 > U443 > U452 > ok > U612
top > active1 > U443 > U452 > ok > U732
top > active1 > U513 > isPalListKind1 > ok > U112
top > active1 > U513 > isPalListKind1 > ok > U252
top > active1 > U513 > isPalListKind1 > ok > U533
top > active1 > U513 > isPalListKind1 > ok > U612
top > active1 > U513 > isPalListKind1 > ok > U732
top > active1 > U513 > U523 > U533
top > active1 > U722 > ok > U112
top > active1 > U722 > ok > U252
top > active1 > U722 > ok > U533
top > active1 > U722 > ok > U612
top > active1 > U722 > ok > U732
top > active1 > U812
top > active1 > U912 > isPalListKind1 > ok > U112
top > active1 > U912 > isPalListKind1 > ok > U252
top > active1 > U912 > isPalListKind1 > ok > U533
top > active1 > U912 > isPalListKind1 > ok > U612
top > active1 > U912 > isPalListKind1 > ok > U732
top > active1 > tt > isPalListKind1 > ok > U112
top > active1 > tt > isPalListKind1 > ok > U252
top > active1 > tt > isPalListKind1 > ok > U533
top > active1 > tt > isPalListKind1 > ok > U612
top > active1 > tt > isPalListKind1 > ok > U732
top > active1 > tt > U243 > U252
top > active1 > tt > U322
top > active1 > tt > U433
top > active1 > tt > U523 > U533
top > active1 > tt > U543
top > active1 > tt > U552
top > active1 > tt > U622
top > active1 > tt > U822

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

(298) Obligation:

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

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

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

(299) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


PROPER(U13(X)) → PROPER(X)
PROPER(U26(X)) → PROPER(X)
PROPER(U33(X)) → PROPER(X)
PROPER(isQid(X)) → PROPER(X)
PROPER(U63(X)) → PROPER(X)
PROPER(isPal(X)) → PROPER(X)
PROPER(U74(X)) → PROPER(X)
PROPER(U83(X)) → PROPER(X)
PROPER(isNePal(X)) → PROPER(X)
PROPER(U92(X)) → PROPER(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
PROPER(x1)  =  x1
U13(x1)  =  U13(x1)
isNeList(x1)  =  x1
isList(x1)  =  x1
U26(x1)  =  U26(x1)
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid(x1)
U46(x1)  =  x1
U56(x1)  =  x1
U63(x1)  =  U63(x1)
isPal(x1)  =  isPal(x1)
U74(x1)  =  U74(x1)
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal(x1)
U92(x1)  =  U92(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind(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)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
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)
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)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U91(x1, x2)  =  U91(x1, x2)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > U131 > tt > U331 > mark1
active1 > U131 > tt > isPal1 > mark1
active1 > U131 > tt > U831 > mark1
active1 > U131 > tt > U122 > mark1
active1 > U131 > tt > U252 > mark1
active1 > U131 > tt > U433 > mark1
active1 > U131 > tt > U452 > mark1
active1 > U131 > tt > U523 > mark1
active1 > U131 > tt > U533 > mark1
active1 > U131 > tt > U552 > mark1
active1 > U131 > tt > U622 > mark1
active1 > U131 > tt > U732 > mark1
active1 > U131 > tt > U822 > mark1
active1 > U261 > tt > U331 > mark1
active1 > U261 > tt > isPal1 > mark1
active1 > U261 > tt > U831 > mark1
active1 > U261 > tt > U122 > mark1
active1 > U261 > tt > U252 > mark1
active1 > U261 > tt > U433 > mark1
active1 > U261 > tt > U452 > mark1
active1 > U261 > tt > U523 > mark1
active1 > U261 > tt > U533 > mark1
active1 > U261 > tt > U552 > mark1
active1 > U261 > tt > U622 > mark1
active1 > U261 > tt > U732 > mark1
active1 > U261 > tt > U822 > mark1
active1 > U631 > tt > U331 > mark1
active1 > U631 > tt > isPal1 > mark1
active1 > U631 > tt > U831 > mark1
active1 > U631 > tt > U122 > mark1
active1 > U631 > tt > U252 > mark1
active1 > U631 > tt > U433 > mark1
active1 > U631 > tt > U452 > mark1
active1 > U631 > tt > U523 > mark1
active1 > U631 > tt > U533 > mark1
active1 > U631 > tt > U552 > mark1
active1 > U631 > tt > U622 > mark1
active1 > U631 > tt > U732 > mark1
active1 > U631 > tt > U822 > mark1
active1 > U741 > tt > U331 > mark1
active1 > U741 > tt > isPal1 > mark1
active1 > U741 > tt > U831 > mark1
active1 > U741 > tt > U122 > mark1
active1 > U741 > tt > U252 > mark1
active1 > U741 > tt > U433 > mark1
active1 > U741 > tt > U452 > mark1
active1 > U741 > tt > U523 > mark1
active1 > U741 > tt > U533 > mark1
active1 > U741 > tt > U552 > mark1
active1 > U741 > tt > U622 > mark1
active1 > U741 > tt > U732 > mark1
active1 > U741 > tt > U822 > mark1
active1 > isNePal1 > isPalListKind1 > mark1
active1 > isNePal1 > U612 > mark1
active1 > _2 > U213 > mark1
active1 > _2 > U413 > mark1
active1 > _2 > U513 > U523 > mark1
active1 > U112 > mark1
active1 > U223 > mark1
active1 > U233 > isPalListKind1 > mark1
active1 > U243 > U252 > mark1
active1 > U312 > isPalListKind1 > mark1
active1 > U322 > isQid1 > tt > U331 > mark1
active1 > U322 > isQid1 > tt > isPal1 > mark1
active1 > U322 > isQid1 > tt > U831 > mark1
active1 > U322 > isQid1 > tt > U122 > mark1
active1 > U322 > isQid1 > tt > U252 > mark1
active1 > U322 > isQid1 > tt > U433 > mark1
active1 > U322 > isQid1 > tt > U452 > mark1
active1 > U322 > isQid1 > tt > U523 > mark1
active1 > U322 > isQid1 > tt > U533 > mark1
active1 > U322 > isQid1 > tt > U552 > mark1
active1 > U322 > isQid1 > tt > U622 > mark1
active1 > U322 > isQid1 > tt > U732 > mark1
active1 > U322 > isQid1 > tt > U822 > mark1
active1 > U423 > isPalListKind1 > mark1
active1 > U423 > U433 > mark1
active1 > U443 > U452 > mark1
active1 > U543 > U552 > mark1
active1 > U713 > isPalListKind1 > mark1
active1 > U713 > U722 > isPal1 > mark1
active1 > U713 > U722 > U732 > mark1
active1 > U812 > isPalListKind1 > mark1
active1 > U812 > U822 > mark1
active1 > U912 > U921 > tt > U331 > mark1
active1 > U912 > U921 > tt > isPal1 > mark1
active1 > U912 > U921 > tt > U831 > mark1
active1 > U912 > U921 > tt > U122 > mark1
active1 > U912 > U921 > tt > U252 > mark1
active1 > U912 > U921 > tt > U433 > mark1
active1 > U912 > U921 > tt > U452 > mark1
active1 > U912 > U921 > tt > U523 > mark1
active1 > U912 > U921 > tt > U533 > mark1
active1 > U912 > U921 > tt > U552 > mark1
active1 > U912 > U921 > tt > U622 > mark1
active1 > U912 > U921 > tt > U732 > mark1
active1 > U912 > U921 > tt > U822 > mark1
active1 > U912 > isPalListKind1 > mark1
nil > mark1
a > mark1
e > mark1
i > mark1
o > mark1
u > mark1

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

(300) Obligation:

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

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

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

(301) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


PROPER(isNeList(X)) → PROPER(X)
PROPER(isList(X)) → PROPER(X)
PROPER(U56(X)) → PROPER(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
PROPER(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
isList(x1)  =  isList(x1)
U46(x1)  =  x1
U56(x1)  =  U56(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  U13(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)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(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)
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)
U61(x1, x2)  =  U61(x1)
U62(x1, x2)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  x1
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U74(x1)  =  U74(x1)
U81(x1, x2)  =  x1
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > isNeList1 > U312 > isPalListKind > tt > ok
active1 > isNeList1 > U312 > isPalListKind > U911 > mark1 > top
active1 > isNeList1 > U312 > isPalListKind > U911 > ok
active1 > isNeList1 > U312 > U322 > U331 > mark1 > top
active1 > isNeList1 > U312 > U322 > U331 > tt > ok
active1 > isNeList1 > U413 > U423 > isPalListKind > tt > ok
active1 > isNeList1 > U413 > U423 > isPalListKind > U911 > mark1 > top
active1 > isNeList1 > U413 > U423 > isPalListKind > U911 > ok
active1 > isNeList1 > U413 > U423 > U433 > U443 > isList1 > tt > ok
active1 > isNeList1 > U413 > U423 > U433 > U443 > mark1 > top
active1 > isNeList1 > U513 > U523 > U533 > U543 > U552 > isList1 > tt > ok
active1 > isNeList1 > U513 > U523 > U533 > U543 > U552 > mark1 > top
active1 > U561 > mark1 > top
active1 > U561 > tt > ok
active1 > _2 > U213 > mark1 > top
active1 > _2 > U213 > ok
active1 > _2 > isQid > mark1 > top
active1 > _2 > isQid > tt > ok
active1 > _2 > U911 > mark1 > top
active1 > _2 > U911 > ok
active1 > U112 > U122 > U131 > mark1 > top
active1 > U112 > U122 > U131 > tt > ok
active1 > U112 > isPalListKind > tt > ok
active1 > U112 > isPalListKind > U911 > mark1 > top
active1 > U112 > isPalListKind > U911 > ok
active1 > U223 > mark1 > top
active1 > U223 > ok
active1 > U233 > mark1 > top
active1 > U233 > ok
active1 > U243 > U252 > isList1 > tt > ok
active1 > U243 > U252 > mark1 > top
active1 > U452 > mark1 > top
active1 > U452 > ok
active1 > U611 > mark1 > top
active1 > U611 > ok
active1 > isPal > mark1 > top
active1 > isPal > tt > ok
active1 > U741 > mark1 > top
active1 > U741 > tt > ok
active1 > U831 > mark1 > top
active1 > U831 > tt > ok
active1 > isNePal > ok
active1 > U921 > mark1 > top
active1 > U921 > tt > ok
nil > tt > ok
a > mark1 > top
a > tt > ok
e > tt > ok
i > ok
o > ok
u > ok

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

(302) Obligation:

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

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

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

(303) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


PROPER(U46(X)) → PROPER(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
PROPER(x1)  =  PROPER(x1)
U46(x1)  =  U46(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  x1
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(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)
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)  =  U56(x1)
U61(x1, x2)  =  x1
U62(x1, x2)  =  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)  =  x1
U74(x1)  =  U74(x1)
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  x1
U91(x1, x2)  =  x1
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
PROPER1 > mark1
top > active1 > U461 > tt > U243 > mark1
top > active1 > U461 > tt > U331 > mark1
top > active1 > U461 > tt > ok > _2 > mark1
top > active1 > U461 > tt > ok > U423 > mark1
top > active1 > U461 > tt > ok > U533 > mark1
top > active1 > U112 > isPalListKind > tt > U243 > mark1
top > active1 > U112 > isPalListKind > tt > U331 > mark1
top > active1 > U112 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U112 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U112 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U122 > isNeList1 > U312 > isPalListKind > tt > U243 > mark1
top > active1 > U122 > isNeList1 > U312 > isPalListKind > tt > U331 > mark1
top > active1 > U122 > isNeList1 > U312 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U122 > isNeList1 > U312 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U122 > isNeList1 > U312 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U213 > isPalListKind > tt > U243 > mark1
top > active1 > U213 > isPalListKind > tt > U331 > mark1
top > active1 > U213 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U213 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U213 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U213 > U223 > ok > _2 > mark1
top > active1 > U213 > U223 > ok > U423 > mark1
top > active1 > U213 > U223 > ok > U533 > mark1
top > active1 > U233 > isPalListKind > tt > U243 > mark1
top > active1 > U233 > isPalListKind > tt > U331 > mark1
top > active1 > U233 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U233 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U233 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U252 > ok > _2 > mark1
top > active1 > U252 > ok > U423 > mark1
top > active1 > U252 > ok > U533 > mark1
top > active1 > U321 > U331 > mark1
top > active1 > U321 > ok > _2 > mark1
top > active1 > U321 > ok > U423 > mark1
top > active1 > U321 > ok > U533 > mark1
top > active1 > isQid > tt > U243 > mark1
top > active1 > isQid > tt > U331 > mark1
top > active1 > isQid > tt > ok > _2 > mark1
top > active1 > isQid > tt > ok > U423 > mark1
top > active1 > isQid > tt > ok > U533 > mark1
top > active1 > U413 > isPalListKind > tt > U243 > mark1
top > active1 > U413 > isPalListKind > tt > U331 > mark1
top > active1 > U413 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U413 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U413 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U433 > isPalListKind > tt > U243 > mark1
top > active1 > U433 > isPalListKind > tt > U331 > mark1
top > active1 > U433 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U433 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U433 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U443 > ok > _2 > mark1
top > active1 > U443 > ok > U423 > mark1
top > active1 > U443 > ok > U533 > mark1
top > active1 > U452 > isNeList1 > U312 > isPalListKind > tt > U243 > mark1
top > active1 > U452 > isNeList1 > U312 > isPalListKind > tt > U331 > mark1
top > active1 > U452 > isNeList1 > U312 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U452 > isNeList1 > U312 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U452 > isNeList1 > U312 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U513 > isPalListKind > tt > U243 > mark1
top > active1 > U513 > isPalListKind > tt > U331 > mark1
top > active1 > U513 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U513 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U513 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U523 > isPalListKind > tt > U243 > mark1
top > active1 > U523 > isPalListKind > tt > U331 > mark1
top > active1 > U523 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U523 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U523 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U543 > ok > _2 > mark1
top > active1 > U543 > ok > U423 > mark1
top > active1 > U543 > ok > U533 > mark1
top > active1 > U552 > ok > _2 > mark1
top > active1 > U552 > ok > U423 > mark1
top > active1 > U552 > ok > U533 > mark1
top > active1 > U561 > tt > U243 > mark1
top > active1 > U561 > tt > U331 > mark1
top > active1 > U561 > tt > ok > _2 > mark1
top > active1 > U561 > tt > ok > U423 > mark1
top > active1 > U561 > tt > ok > U533 > mark1
top > active1 > U713 > isPalListKind > tt > U243 > mark1
top > active1 > U713 > isPalListKind > tt > U331 > mark1
top > active1 > U713 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U713 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U713 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U722 > ok > _2 > mark1
top > active1 > U722 > ok > U423 > mark1
top > active1 > U722 > ok > U533 > mark1
top > active1 > U732 > isPalListKind > tt > U243 > mark1
top > active1 > U732 > isPalListKind > tt > U331 > mark1
top > active1 > U732 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U732 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U732 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U732 > U741 > tt > U243 > mark1
top > active1 > U732 > U741 > tt > U331 > mark1
top > active1 > U732 > U741 > tt > ok > _2 > mark1
top > active1 > U732 > U741 > tt > ok > U423 > mark1
top > active1 > U732 > U741 > tt > ok > U533 > mark1
top > active1 > U812 > isPalListKind > tt > U243 > mark1
top > active1 > U812 > isPalListKind > tt > U331 > mark1
top > active1 > U812 > isPalListKind > tt > ok > _2 > mark1
top > active1 > U812 > isPalListKind > tt > ok > U423 > mark1
top > active1 > U812 > isPalListKind > tt > ok > U533 > mark1
top > active1 > U822 > ok > _2 > mark1
top > active1 > U822 > ok > U423 > mark1
top > active1 > U822 > ok > U533 > mark1
top > active1 > U921 > tt > U243 > mark1
top > active1 > U921 > tt > U331 > mark1
top > active1 > U921 > tt > ok > _2 > mark1
top > active1 > U921 > tt > ok > U423 > mark1
top > active1 > U921 > tt > ok > U533 > mark1
top > proper1 > U461 > tt > U243 > mark1
top > proper1 > U461 > tt > U331 > mark1
top > proper1 > U461 > tt > ok > _2 > mark1
top > proper1 > U461 > tt > ok > U423 > mark1
top > proper1 > U461 > tt > ok > U533 > mark1
top > proper1 > nil > mark1
top > proper1 > U112 > isPalListKind > tt > U243 > mark1
top > proper1 > U112 > isPalListKind > tt > U331 > mark1
top > proper1 > U112 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U112 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U112 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U122 > isNeList1 > U312 > isPalListKind > tt > U243 > mark1
top > proper1 > U122 > isNeList1 > U312 > isPalListKind > tt > U331 > mark1
top > proper1 > U122 > isNeList1 > U312 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U122 > isNeList1 > U312 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U122 > isNeList1 > U312 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U213 > isPalListKind > tt > U243 > mark1
top > proper1 > U213 > isPalListKind > tt > U331 > mark1
top > proper1 > U213 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U213 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U213 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U213 > U223 > ok > _2 > mark1
top > proper1 > U213 > U223 > ok > U423 > mark1
top > proper1 > U213 > U223 > ok > U533 > mark1
top > proper1 > U233 > isPalListKind > tt > U243 > mark1
top > proper1 > U233 > isPalListKind > tt > U331 > mark1
top > proper1 > U233 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U233 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U233 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U252 > ok > _2 > mark1
top > proper1 > U252 > ok > U423 > mark1
top > proper1 > U252 > ok > U533 > mark1
top > proper1 > U321 > U331 > mark1
top > proper1 > U321 > ok > _2 > mark1
top > proper1 > U321 > ok > U423 > mark1
top > proper1 > U321 > ok > U533 > mark1
top > proper1 > isQid > tt > U243 > mark1
top > proper1 > isQid > tt > U331 > mark1
top > proper1 > isQid > tt > ok > _2 > mark1
top > proper1 > isQid > tt > ok > U423 > mark1
top > proper1 > isQid > tt > ok > U533 > mark1
top > proper1 > U413 > isPalListKind > tt > U243 > mark1
top > proper1 > U413 > isPalListKind > tt > U331 > mark1
top > proper1 > U413 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U413 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U413 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U433 > isPalListKind > tt > U243 > mark1
top > proper1 > U433 > isPalListKind > tt > U331 > mark1
top > proper1 > U433 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U433 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U433 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U443 > ok > _2 > mark1
top > proper1 > U443 > ok > U423 > mark1
top > proper1 > U443 > ok > U533 > mark1
top > proper1 > U452 > isNeList1 > U312 > isPalListKind > tt > U243 > mark1
top > proper1 > U452 > isNeList1 > U312 > isPalListKind > tt > U331 > mark1
top > proper1 > U452 > isNeList1 > U312 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U452 > isNeList1 > U312 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U452 > isNeList1 > U312 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U513 > isPalListKind > tt > U243 > mark1
top > proper1 > U513 > isPalListKind > tt > U331 > mark1
top > proper1 > U513 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U513 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U513 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U523 > isPalListKind > tt > U243 > mark1
top > proper1 > U523 > isPalListKind > tt > U331 > mark1
top > proper1 > U523 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U523 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U523 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U543 > ok > _2 > mark1
top > proper1 > U543 > ok > U423 > mark1
top > proper1 > U543 > ok > U533 > mark1
top > proper1 > U552 > ok > _2 > mark1
top > proper1 > U552 > ok > U423 > mark1
top > proper1 > U552 > ok > U533 > mark1
top > proper1 > U561 > tt > U243 > mark1
top > proper1 > U561 > tt > U331 > mark1
top > proper1 > U561 > tt > ok > _2 > mark1
top > proper1 > U561 > tt > ok > U423 > mark1
top > proper1 > U561 > tt > ok > U533 > mark1
top > proper1 > U713 > isPalListKind > tt > U243 > mark1
top > proper1 > U713 > isPalListKind > tt > U331 > mark1
top > proper1 > U713 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U713 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U713 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U722 > ok > _2 > mark1
top > proper1 > U722 > ok > U423 > mark1
top > proper1 > U722 > ok > U533 > mark1
top > proper1 > U732 > isPalListKind > tt > U243 > mark1
top > proper1 > U732 > isPalListKind > tt > U331 > mark1
top > proper1 > U732 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U732 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U732 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U732 > U741 > tt > U243 > mark1
top > proper1 > U732 > U741 > tt > U331 > mark1
top > proper1 > U732 > U741 > tt > ok > _2 > mark1
top > proper1 > U732 > U741 > tt > ok > U423 > mark1
top > proper1 > U732 > U741 > tt > ok > U533 > mark1
top > proper1 > U812 > isPalListKind > tt > U243 > mark1
top > proper1 > U812 > isPalListKind > tt > U331 > mark1
top > proper1 > U812 > isPalListKind > tt > ok > _2 > mark1
top > proper1 > U812 > isPalListKind > tt > ok > U423 > mark1
top > proper1 > U812 > isPalListKind > tt > ok > U533 > mark1
top > proper1 > U822 > ok > _2 > mark1
top > proper1 > U822 > ok > U423 > mark1
top > proper1 > U822 > ok > U533 > mark1
top > proper1 > U921 > tt > U243 > mark1
top > proper1 > U921 > tt > U331 > mark1
top > proper1 > U921 > tt > ok > _2 > mark1
top > proper1 > U921 > tt > ok > U423 > mark1
top > proper1 > U921 > tt > ok > U533 > mark1
top > proper1 > a > mark1
top > proper1 > e > mark1
top > proper1 > i > mark1
top > proper1 > o > mark1
top > proper1 > u > mark1

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

(304) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(305) PisEmptyProof (EQUIVALENT transformation)

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

(306) TRUE

(307) Obligation:

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

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

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

(308) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ACTIVE(__(X1, X2)) → ACTIVE(X2)
ACTIVE(__(X1, X2)) → ACTIVE(X1)
ACTIVE(U11(X1, X2)) → ACTIVE(X1)
ACTIVE(U12(X1, X2)) → ACTIVE(X1)
ACTIVE(U21(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U22(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U23(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U24(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U25(X1, X2)) → ACTIVE(X1)
ACTIVE(U31(X1, X2)) → ACTIVE(X1)
ACTIVE(U41(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U42(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U43(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U44(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U45(X1, X2)) → ACTIVE(X1)
ACTIVE(U46(X)) → ACTIVE(X)
ACTIVE(U51(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U52(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U53(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U54(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U55(X1, X2)) → ACTIVE(X1)
ACTIVE(U61(X1, X2)) → ACTIVE(X1)
ACTIVE(U71(X1, X2, X3)) → ACTIVE(X1)
ACTIVE(U72(X1, X2)) → ACTIVE(X1)
ACTIVE(U73(X1, X2)) → ACTIVE(X1)
ACTIVE(U81(X1, X2)) → ACTIVE(X1)
ACTIVE(U82(X1, X2)) → ACTIVE(X1)
ACTIVE(U91(X1, X2)) → ACTIVE(X1)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ACTIVE(x1)  =  ACTIVE(x1)
__(x1, x2)  =  __(x1, x2)
U11(x1, x2)  =  U11(x1, x2)
U12(x1, x2)  =  U12(x1, x2)
U13(x1)  =  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)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  x1
U33(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(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)  =  x1
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1
active(x1)  =  active(x1)
mark(x1)  =  mark(x1)
nil  =  nil
tt  =  tt
isPalListKind(x1)  =  isPalListKind(x1)
isNeList(x1)  =  isNeList(x1)
isList(x1)  =  isList(x1)
isQid(x1)  =  isQid
isPal(x1)  =  isPal(x1)
isNePal(x1)  =  isNePal(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > _2 > mark1
active1 > _2 > ok > isList1
active1 > U112 > U122 > mark1
active1 > U112 > U122 > isNeList1 > ok > isList1
active1 > U213 > mark1
active1 > U213 > ok > isList1
active1 > U223 > isPalListKind1 > U912 > mark1
active1 > U223 > isPalListKind1 > U912 > ok > isList1
active1 > U223 > isPalListKind1 > tt > U122 > mark1
active1 > U223 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
active1 > U223 > isPalListKind1 > tt > U243 > mark1
active1 > U223 > isPalListKind1 > tt > U243 > ok > isList1
active1 > U223 > isPalListKind1 > tt > U252 > mark1
active1 > U223 > isPalListKind1 > tt > U252 > ok > isList1
active1 > U223 > isPalListKind1 > tt > U533 > mark1
active1 > U223 > isPalListKind1 > tt > U533 > ok > isList1
active1 > U233 > isPalListKind1 > U912 > mark1
active1 > U233 > isPalListKind1 > U912 > ok > isList1
active1 > U233 > isPalListKind1 > tt > U122 > mark1
active1 > U233 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
active1 > U233 > isPalListKind1 > tt > U243 > mark1
active1 > U233 > isPalListKind1 > tt > U243 > ok > isList1
active1 > U233 > isPalListKind1 > tt > U252 > mark1
active1 > U233 > isPalListKind1 > tt > U252 > ok > isList1
active1 > U233 > isPalListKind1 > tt > U533 > mark1
active1 > U233 > isPalListKind1 > tt > U533 > ok > isList1
active1 > U312 > mark1
active1 > U312 > ok > isList1
active1 > U413 > isPalListKind1 > U912 > mark1
active1 > U413 > isPalListKind1 > U912 > ok > isList1
active1 > U413 > isPalListKind1 > tt > U122 > mark1
active1 > U413 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
active1 > U413 > isPalListKind1 > tt > U243 > mark1
active1 > U413 > isPalListKind1 > tt > U243 > ok > isList1
active1 > U413 > isPalListKind1 > tt > U252 > mark1
active1 > U413 > isPalListKind1 > tt > U252 > ok > isList1
active1 > U413 > isPalListKind1 > tt > U533 > mark1
active1 > U413 > isPalListKind1 > tt > U533 > ok > isList1
active1 > U423 > U433 > isPalListKind1 > U912 > mark1
active1 > U423 > U433 > isPalListKind1 > U912 > ok > isList1
active1 > U423 > U433 > isPalListKind1 > tt > U122 > mark1
active1 > U423 > U433 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
active1 > U423 > U433 > isPalListKind1 > tt > U243 > mark1
active1 > U423 > U433 > isPalListKind1 > tt > U243 > ok > isList1
active1 > U423 > U433 > isPalListKind1 > tt > U252 > mark1
active1 > U423 > U433 > isPalListKind1 > tt > U252 > ok > isList1
active1 > U423 > U433 > isPalListKind1 > tt > U533 > mark1
active1 > U423 > U433 > isPalListKind1 > tt > U533 > ok > isList1
active1 > U443 > U452 > mark1
active1 > U443 > U452 > isNeList1 > ok > isList1
active1 > U461 > tt > U122 > mark1
active1 > U461 > tt > U122 > isNeList1 > ok > isList1
active1 > U461 > tt > U243 > mark1
active1 > U461 > tt > U243 > ok > isList1
active1 > U461 > tt > U252 > mark1
active1 > U461 > tt > U252 > ok > isList1
active1 > U461 > tt > U533 > mark1
active1 > U461 > tt > U533 > ok > isList1
active1 > U513 > mark1
active1 > U513 > ok > isList1
active1 > U523 > isPalListKind1 > U912 > mark1
active1 > U523 > isPalListKind1 > U912 > ok > isList1
active1 > U523 > isPalListKind1 > tt > U122 > mark1
active1 > U523 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
active1 > U523 > isPalListKind1 > tt > U243 > mark1
active1 > U523 > isPalListKind1 > tt > U243 > ok > isList1
active1 > U523 > isPalListKind1 > tt > U252 > mark1
active1 > U523 > isPalListKind1 > tt > U252 > ok > isList1
active1 > U523 > isPalListKind1 > tt > U533 > mark1
active1 > U523 > isPalListKind1 > tt > U533 > ok > isList1
active1 > U543 > mark1
active1 > U543 > isNeList1 > ok > isList1
active1 > U552 > mark1
active1 > U552 > ok > isList1
active1 > isPal1 > U812 > U822 > mark1
active1 > isPal1 > U812 > U822 > ok > isList1
active1 > isPal1 > isPalListKind1 > U912 > mark1
active1 > isPal1 > isPalListKind1 > U912 > ok > isList1
active1 > isPal1 > isPalListKind1 > tt > U122 > mark1
active1 > isPal1 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
active1 > isPal1 > isPalListKind1 > tt > U243 > mark1
active1 > isPal1 > isPalListKind1 > tt > U243 > ok > isList1
active1 > isPal1 > isPalListKind1 > tt > U252 > mark1
active1 > isPal1 > isPalListKind1 > tt > U252 > ok > isList1
active1 > isPal1 > isPalListKind1 > tt > U533 > mark1
active1 > isPal1 > isPalListKind1 > tt > U533 > ok > isList1
active1 > isNePal1 > U612 > mark1
active1 > isNePal1 > U612 > ok > isList1
active1 > isNePal1 > U713 > U722 > U732 > mark1
active1 > isNePal1 > U713 > U722 > U732 > ok > isList1
active1 > isNePal1 > isQid > mark1
active1 > isNePal1 > isQid > ok > isList1
proper1 > _2 > mark1
proper1 > _2 > ok > isList1
proper1 > U112 > U122 > mark1
proper1 > U112 > U122 > isNeList1 > ok > isList1
proper1 > U213 > mark1
proper1 > U213 > ok > isList1
proper1 > U223 > isPalListKind1 > U912 > mark1
proper1 > U223 > isPalListKind1 > U912 > ok > isList1
proper1 > U223 > isPalListKind1 > tt > U122 > mark1
proper1 > U223 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
proper1 > U223 > isPalListKind1 > tt > U243 > mark1
proper1 > U223 > isPalListKind1 > tt > U243 > ok > isList1
proper1 > U223 > isPalListKind1 > tt > U252 > mark1
proper1 > U223 > isPalListKind1 > tt > U252 > ok > isList1
proper1 > U223 > isPalListKind1 > tt > U533 > mark1
proper1 > U223 > isPalListKind1 > tt > U533 > ok > isList1
proper1 > U233 > isPalListKind1 > U912 > mark1
proper1 > U233 > isPalListKind1 > U912 > ok > isList1
proper1 > U233 > isPalListKind1 > tt > U122 > mark1
proper1 > U233 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
proper1 > U233 > isPalListKind1 > tt > U243 > mark1
proper1 > U233 > isPalListKind1 > tt > U243 > ok > isList1
proper1 > U233 > isPalListKind1 > tt > U252 > mark1
proper1 > U233 > isPalListKind1 > tt > U252 > ok > isList1
proper1 > U233 > isPalListKind1 > tt > U533 > mark1
proper1 > U233 > isPalListKind1 > tt > U533 > ok > isList1
proper1 > U312 > mark1
proper1 > U312 > ok > isList1
proper1 > U413 > isPalListKind1 > U912 > mark1
proper1 > U413 > isPalListKind1 > U912 > ok > isList1
proper1 > U413 > isPalListKind1 > tt > U122 > mark1
proper1 > U413 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
proper1 > U413 > isPalListKind1 > tt > U243 > mark1
proper1 > U413 > isPalListKind1 > tt > U243 > ok > isList1
proper1 > U413 > isPalListKind1 > tt > U252 > mark1
proper1 > U413 > isPalListKind1 > tt > U252 > ok > isList1
proper1 > U413 > isPalListKind1 > tt > U533 > mark1
proper1 > U413 > isPalListKind1 > tt > U533 > ok > isList1
proper1 > U423 > U433 > isPalListKind1 > U912 > mark1
proper1 > U423 > U433 > isPalListKind1 > U912 > ok > isList1
proper1 > U423 > U433 > isPalListKind1 > tt > U122 > mark1
proper1 > U423 > U433 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
proper1 > U423 > U433 > isPalListKind1 > tt > U243 > mark1
proper1 > U423 > U433 > isPalListKind1 > tt > U243 > ok > isList1
proper1 > U423 > U433 > isPalListKind1 > tt > U252 > mark1
proper1 > U423 > U433 > isPalListKind1 > tt > U252 > ok > isList1
proper1 > U423 > U433 > isPalListKind1 > tt > U533 > mark1
proper1 > U423 > U433 > isPalListKind1 > tt > U533 > ok > isList1
proper1 > U443 > U452 > mark1
proper1 > U443 > U452 > isNeList1 > ok > isList1
proper1 > U461 > tt > U122 > mark1
proper1 > U461 > tt > U122 > isNeList1 > ok > isList1
proper1 > U461 > tt > U243 > mark1
proper1 > U461 > tt > U243 > ok > isList1
proper1 > U461 > tt > U252 > mark1
proper1 > U461 > tt > U252 > ok > isList1
proper1 > U461 > tt > U533 > mark1
proper1 > U461 > tt > U533 > ok > isList1
proper1 > U513 > mark1
proper1 > U513 > ok > isList1
proper1 > U523 > isPalListKind1 > U912 > mark1
proper1 > U523 > isPalListKind1 > U912 > ok > isList1
proper1 > U523 > isPalListKind1 > tt > U122 > mark1
proper1 > U523 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
proper1 > U523 > isPalListKind1 > tt > U243 > mark1
proper1 > U523 > isPalListKind1 > tt > U243 > ok > isList1
proper1 > U523 > isPalListKind1 > tt > U252 > mark1
proper1 > U523 > isPalListKind1 > tt > U252 > ok > isList1
proper1 > U523 > isPalListKind1 > tt > U533 > mark1
proper1 > U523 > isPalListKind1 > tt > U533 > ok > isList1
proper1 > U543 > mark1
proper1 > U543 > isNeList1 > ok > isList1
proper1 > U552 > mark1
proper1 > U552 > ok > isList1
proper1 > nil
proper1 > isPal1 > U812 > U822 > mark1
proper1 > isPal1 > U812 > U822 > ok > isList1
proper1 > isPal1 > isPalListKind1 > U912 > mark1
proper1 > isPal1 > isPalListKind1 > U912 > ok > isList1
proper1 > isPal1 > isPalListKind1 > tt > U122 > mark1
proper1 > isPal1 > isPalListKind1 > tt > U122 > isNeList1 > ok > isList1
proper1 > isPal1 > isPalListKind1 > tt > U243 > mark1
proper1 > isPal1 > isPalListKind1 > tt > U243 > ok > isList1
proper1 > isPal1 > isPalListKind1 > tt > U252 > mark1
proper1 > isPal1 > isPalListKind1 > tt > U252 > ok > isList1
proper1 > isPal1 > isPalListKind1 > tt > U533 > mark1
proper1 > isPal1 > isPalListKind1 > tt > U533 > ok > isList1
proper1 > isNePal1 > U612 > mark1
proper1 > isNePal1 > U612 > ok > isList1
proper1 > isNePal1 > U713 > U722 > U732 > mark1
proper1 > isNePal1 > U713 > U722 > U732 > ok > isList1
proper1 > isNePal1 > isQid > mark1
proper1 > isNePal1 > isQid > ok > isList1
proper1 > a
proper1 > e > tt > U122 > mark1
proper1 > e > tt > U122 > isNeList1 > ok > isList1
proper1 > e > tt > U243 > mark1
proper1 > e > tt > U243 > ok > isList1
proper1 > e > tt > U252 > mark1
proper1 > e > tt > U252 > ok > isList1
proper1 > e > tt > U533 > mark1
proper1 > e > tt > U533 > ok > isList1
proper1 > i
proper1 > o
proper1 > 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

(309) Obligation:

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

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

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

(310) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ACTIVE(U26(X)) → ACTIVE(X)
ACTIVE(U32(X1, X2)) → ACTIVE(X1)
ACTIVE(U33(X)) → ACTIVE(X)
ACTIVE(U56(X)) → ACTIVE(X)
ACTIVE(U92(X)) → ACTIVE(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ACTIVE(x1)  =  x1
U13(x1)  =  x1
U26(x1)  =  U26(x1)
U32(x1, x2)  =  U32(x1)
U33(x1)  =  U33(x1)
U56(x1)  =  U56(x1)
U62(x1, x2)  =  x1
U63(x1)  =  x1
U74(x1)  =  x1
U83(x1)  =  x1
U92(x1)  =  U92(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  x1
isPalListKind(x1)  =  isPalListKind
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  U23(x1)
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U31(x1, x2)  =  U31(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  U41(x1)
U42(x1, x2, x3)  =  x1
U43(x1, x2, x3)  =  U43(x1)
U44(x1, x2, x3)  =  x1
U45(x1, x2)  =  U45(x1)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1)
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  x1
U54(x1, x2, x3)  =  x1
U55(x1, x2)  =  U55(x1)
U61(x1, x2)  =  U61(x1)
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  x1
isPal(x1)  =  isPal
U81(x1, x2)  =  U81(x1)
U82(x1, x2)  =  x1
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  proper(x1)
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
active1 > U261 > tt > U331 > mark1
active1 > U261 > tt > U331 > ok
active1 > U261 > tt > U921 > mark1
active1 > U261 > tt > U921 > ok
active1 > U261 > tt > U251 > mark1
active1 > U261 > tt > U251 > ok
active1 > U261 > tt > U431 > mark1
active1 > U261 > tt > U431 > ok
active1 > U261 > tt > U721 > mark1
active1 > U261 > tt > U721 > ok
active1 > U321 > isQid > tt > U331 > mark1
active1 > U321 > isQid > tt > U331 > ok
active1 > U321 > isQid > tt > U921 > mark1
active1 > U321 > isQid > tt > U921 > ok
active1 > U321 > isQid > tt > U251 > mark1
active1 > U321 > isQid > tt > U251 > ok
active1 > U321 > isQid > tt > U431 > mark1
active1 > U321 > isQid > tt > U431 > ok
active1 > U321 > isQid > tt > U721 > mark1
active1 > U321 > isQid > tt > U721 > ok
active1 > U561 > tt > U331 > mark1
active1 > U561 > tt > U331 > ok
active1 > U561 > tt > U921 > mark1
active1 > U561 > tt > U921 > ok
active1 > U561 > tt > U251 > mark1
active1 > U561 > tt > U251 > ok
active1 > U561 > tt > U431 > mark1
active1 > U561 > tt > U431 > ok
active1 > U561 > tt > U721 > mark1
active1 > U561 > tt > U721 > ok
active1 > _2 > mark1
active1 > _2 > ok
active1 > isNeList > U311 > mark1
active1 > isNeList > U311 > ok
active1 > isNeList > U411 > mark1
active1 > isNeList > U411 > ok
active1 > isNeList > U511 > mark1
active1 > isNeList > U511 > ok
active1 > U211 > isPalListKind > tt > U331 > mark1
active1 > U211 > isPalListKind > tt > U331 > ok
active1 > U211 > isPalListKind > tt > U921 > mark1
active1 > U211 > isPalListKind > tt > U921 > ok
active1 > U211 > isPalListKind > tt > U251 > mark1
active1 > U211 > isPalListKind > tt > U251 > ok
active1 > U211 > isPalListKind > tt > U431 > mark1
active1 > U211 > isPalListKind > tt > U431 > ok
active1 > U211 > isPalListKind > tt > U721 > mark1
active1 > U211 > isPalListKind > tt > U721 > ok
active1 > U211 > isPalListKind > U911 > U921 > mark1
active1 > U211 > isPalListKind > U911 > U921 > ok
active1 > U231 > mark1
active1 > U231 > ok
active1 > U241 > U251 > mark1
active1 > U241 > U251 > ok
active1 > isList > tt > U331 > mark1
active1 > isList > tt > U331 > ok
active1 > isList > tt > U921 > mark1
active1 > isList > tt > U921 > ok
active1 > isList > tt > U251 > mark1
active1 > isList > tt > U251 > ok
active1 > isList > tt > U431 > mark1
active1 > isList > tt > U431 > ok
active1 > isList > tt > U721 > mark1
active1 > isList > tt > U721 > ok
active1 > U451 > mark1
active1 > U451 > ok
active1 > U551 > mark1
active1 > U551 > ok
active1 > U611 > isPalListKind > tt > U331 > mark1
active1 > U611 > isPalListKind > tt > U331 > ok
active1 > U611 > isPalListKind > tt > U921 > mark1
active1 > U611 > isPalListKind > tt > U921 > ok
active1 > U611 > isPalListKind > tt > U251 > mark1
active1 > U611 > isPalListKind > tt > U251 > ok
active1 > U611 > isPalListKind > tt > U431 > mark1
active1 > U611 > isPalListKind > tt > U431 > ok
active1 > U611 > isPalListKind > tt > U721 > mark1
active1 > U611 > isPalListKind > tt > U721 > ok
active1 > U611 > isPalListKind > U911 > U921 > mark1
active1 > U611 > isPalListKind > U911 > U921 > ok
active1 > isPal > tt > U331 > mark1
active1 > isPal > tt > U331 > ok
active1 > isPal > tt > U921 > mark1
active1 > isPal > tt > U921 > ok
active1 > isPal > tt > U251 > mark1
active1 > isPal > tt > U251 > ok
active1 > isPal > tt > U431 > mark1
active1 > isPal > tt > U431 > ok
active1 > isPal > tt > U721 > mark1
active1 > isPal > tt > U721 > ok
active1 > isPal > U811 > mark1
active1 > isPal > U811 > ok
active1 > isNePal > isPalListKind > tt > U331 > mark1
active1 > isNePal > isPalListKind > tt > U331 > ok
active1 > isNePal > isPalListKind > tt > U921 > mark1
active1 > isNePal > isPalListKind > tt > U921 > ok
active1 > isNePal > isPalListKind > tt > U251 > mark1
active1 > isNePal > isPalListKind > tt > U251 > ok
active1 > isNePal > isPalListKind > tt > U431 > mark1
active1 > isNePal > isPalListKind > tt > U431 > ok
active1 > isNePal > isPalListKind > tt > U721 > mark1
active1 > isNePal > isPalListKind > tt > U721 > ok
active1 > isNePal > isPalListKind > U911 > U921 > mark1
active1 > isNePal > isPalListKind > U911 > U921 > ok
u > tt > U331 > mark1
u > tt > U331 > ok
u > tt > U921 > mark1
u > tt > U921 > ok
u > tt > U251 > mark1
u > tt > U251 > ok
u > tt > U431 > mark1
u > tt > U431 > ok
u > tt > U721 > mark1
u > tt > U721 > ok
proper1 > U261 > tt > U331 > mark1
proper1 > U261 > tt > U331 > ok
proper1 > U261 > tt > U921 > mark1
proper1 > U261 > tt > U921 > ok
proper1 > U261 > tt > U251 > mark1
proper1 > U261 > tt > U251 > ok
proper1 > U261 > tt > U431 > mark1
proper1 > U261 > tt > U431 > ok
proper1 > U261 > tt > U721 > mark1
proper1 > U261 > tt > U721 > ok
proper1 > U321 > isQid > tt > U331 > mark1
proper1 > U321 > isQid > tt > U331 > ok
proper1 > U321 > isQid > tt > U921 > mark1
proper1 > U321 > isQid > tt > U921 > ok
proper1 > U321 > isQid > tt > U251 > mark1
proper1 > U321 > isQid > tt > U251 > ok
proper1 > U321 > isQid > tt > U431 > mark1
proper1 > U321 > isQid > tt > U431 > ok
proper1 > U321 > isQid > tt > U721 > mark1
proper1 > U321 > isQid > tt > U721 > ok
proper1 > U561 > tt > U331 > mark1
proper1 > U561 > tt > U331 > ok
proper1 > U561 > tt > U921 > mark1
proper1 > U561 > tt > U921 > ok
proper1 > U561 > tt > U251 > mark1
proper1 > U561 > tt > U251 > ok
proper1 > U561 > tt > U431 > mark1
proper1 > U561 > tt > U431 > ok
proper1 > U561 > tt > U721 > mark1
proper1 > U561 > tt > U721 > ok
proper1 > _2 > mark1
proper1 > _2 > ok
proper1 > nil
proper1 > isNeList > U311 > mark1
proper1 > isNeList > U311 > ok
proper1 > isNeList > U411 > mark1
proper1 > isNeList > U411 > ok
proper1 > isNeList > U511 > mark1
proper1 > isNeList > U511 > ok
proper1 > U211 > isPalListKind > tt > U331 > mark1
proper1 > U211 > isPalListKind > tt > U331 > ok
proper1 > U211 > isPalListKind > tt > U921 > mark1
proper1 > U211 > isPalListKind > tt > U921 > ok
proper1 > U211 > isPalListKind > tt > U251 > mark1
proper1 > U211 > isPalListKind > tt > U251 > ok
proper1 > U211 > isPalListKind > tt > U431 > mark1
proper1 > U211 > isPalListKind > tt > U431 > ok
proper1 > U211 > isPalListKind > tt > U721 > mark1
proper1 > U211 > isPalListKind > tt > U721 > ok
proper1 > U211 > isPalListKind > U911 > U921 > mark1
proper1 > U211 > isPalListKind > U911 > U921 > ok
proper1 > U231 > mark1
proper1 > U231 > ok
proper1 > U241 > U251 > mark1
proper1 > U241 > U251 > ok
proper1 > isList > tt > U331 > mark1
proper1 > isList > tt > U331 > ok
proper1 > isList > tt > U921 > mark1
proper1 > isList > tt > U921 > ok
proper1 > isList > tt > U251 > mark1
proper1 > isList > tt > U251 > ok
proper1 > isList > tt > U431 > mark1
proper1 > isList > tt > U431 > ok
proper1 > isList > tt > U721 > mark1
proper1 > isList > tt > U721 > ok
proper1 > U451 > mark1
proper1 > U451 > ok
proper1 > U551 > mark1
proper1 > U551 > ok
proper1 > U611 > isPalListKind > tt > U331 > mark1
proper1 > U611 > isPalListKind > tt > U331 > ok
proper1 > U611 > isPalListKind > tt > U921 > mark1
proper1 > U611 > isPalListKind > tt > U921 > ok
proper1 > U611 > isPalListKind > tt > U251 > mark1
proper1 > U611 > isPalListKind > tt > U251 > ok
proper1 > U611 > isPalListKind > tt > U431 > mark1
proper1 > U611 > isPalListKind > tt > U431 > ok
proper1 > U611 > isPalListKind > tt > U721 > mark1
proper1 > U611 > isPalListKind > tt > U721 > ok
proper1 > U611 > isPalListKind > U911 > U921 > mark1
proper1 > U611 > isPalListKind > U911 > U921 > ok
proper1 > isPal > tt > U331 > mark1
proper1 > isPal > tt > U331 > ok
proper1 > isPal > tt > U921 > mark1
proper1 > isPal > tt > U921 > ok
proper1 > isPal > tt > U251 > mark1
proper1 > isPal > tt > U251 > ok
proper1 > isPal > tt > U431 > mark1
proper1 > isPal > tt > U431 > ok
proper1 > isPal > tt > U721 > mark1
proper1 > isPal > tt > U721 > ok
proper1 > isPal > U811 > mark1
proper1 > isPal > U811 > ok
proper1 > isNePal > isPalListKind > tt > U331 > mark1
proper1 > isNePal > isPalListKind > tt > U331 > ok
proper1 > isNePal > isPalListKind > tt > U921 > mark1
proper1 > isNePal > isPalListKind > tt > U921 > ok
proper1 > isNePal > isPalListKind > tt > U251 > mark1
proper1 > isNePal > isPalListKind > tt > U251 > ok
proper1 > isNePal > isPalListKind > tt > U431 > mark1
proper1 > isNePal > isPalListKind > tt > U431 > ok
proper1 > isNePal > isPalListKind > tt > U721 > mark1
proper1 > isNePal > isPalListKind > tt > U721 > ok
proper1 > isNePal > isPalListKind > U911 > U921 > mark1
proper1 > isNePal > isPalListKind > U911 > U921 > ok
proper1 > a > mark1
proper1 > a > ok
proper1 > e
proper1 > i
proper1 > o > tt > U331 > mark1
proper1 > o > tt > U331 > ok
proper1 > o > tt > U921 > mark1
proper1 > o > tt > U921 > ok
proper1 > o > tt > U251 > mark1
proper1 > o > tt > U251 > ok
proper1 > o > tt > U431 > mark1
proper1 > o > tt > U431 > ok
proper1 > o > tt > U721 > mark1
proper1 > o > tt > U721 > ok

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

(311) Obligation:

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

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

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

(312) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ACTIVE(U62(X1, X2)) → ACTIVE(X1)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ACTIVE(x1)  =  x1
U13(x1)  =  x1
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U74(x1)  =  x1
U83(x1)  =  x1
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  x1
tt  =  tt
U12(x1, x2)  =  U12(x1)
isPalListKind(x1)  =  isPalListKind
isNeList(x1)  =  isNeList
U21(x1, x2, x3)  =  U21(x1)
U22(x1, x2, x3)  =  x1
U23(x1, x2, x3)  =  x1
U24(x1, x2, x3)  =  U24(x1)
U25(x1, x2)  =  U25(x1)
isList(x1)  =  isList
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1)
U32(x1, x2)  =  x1
U33(x1)  =  U33(x1)
isQid(x1)  =  isQid
U41(x1, x2, x3)  =  x1
U42(x1, x2, x3)  =  U42(x1)
U43(x1, x2, x3)  =  x1
U44(x1, x2, x3)  =  U44(x1)
U45(x1, x2)  =  x1
U46(x1)  =  x1
U51(x1, x2, x3)  =  x1
U52(x1, x2, x3)  =  x1
U53(x1, x2, x3)  =  U53(x1)
U54(x1, x2, x3)  =  U54(x1)
U55(x1, x2)  =  U55(x1)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U71(x1, x2, x3)  =  U71(x1, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  x1
isPal(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
isNePal(x1)  =  x1
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  ok
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
nil > ok
a > mark1
a > tt > ok
e > ok
i > ok
o > mark1
o > tt > ok
u > mark1
u > tt > ok
top > active1 > _2 > isPalListKind > mark1
top > active1 > _2 > isPalListKind > tt > ok
top > active1 > _2 > U211 > mark1
top > active1 > _2 > U211 > ok
top > active1 > _2 > isQid > mark1
top > active1 > _2 > isQid > tt > ok
top > active1 > _2 > U712 > mark1
top > active1 > _2 > U712 > ok
top > active1 > U121 > isNeList > U311 > mark1
top > active1 > U121 > isNeList > U311 > ok
top > active1 > U241 > U251 > mark1
top > active1 > U241 > U251 > ok
top > active1 > U331 > mark1
top > active1 > U331 > tt > ok
top > active1 > U421 > mark1
top > active1 > U421 > ok
top > active1 > U441 > isList > mark1
top > active1 > U441 > isList > tt > ok
top > active1 > U531 > mark1
top > active1 > U531 > ok
top > active1 > U541 > isNeList > U311 > mark1
top > active1 > U541 > isNeList > U311 > ok
top > active1 > U541 > U551 > mark1
top > active1 > U541 > U551 > ok
top > active1 > U612 > U622 > mark1
top > active1 > U612 > U622 > ok
top > active1 > U722 > mark1
top > active1 > U722 > ok
top > active1 > U812 > U822 > mark1
top > active1 > U812 > U822 > ok
top > active1 > U911 > isPalListKind > mark1
top > active1 > U911 > isPalListKind > tt > ok
top > active1 > U921 > mark1
top > active1 > U921 > tt > ok

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

(313) Obligation:

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

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

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

(314) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
ACTIVE1 > mark1
proper1 > U741 > tt > U122 > mark1
proper1 > U741 > tt > U223 > U233 > mark1
proper1 > U741 > tt > U252 > mark1
proper1 > U741 > tt > U322 > mark1
proper1 > U741 > tt > U331 > mark1
proper1 > U741 > tt > U433 > mark1
proper1 > U741 > tt > U452 > mark1
proper1 > U741 > tt > U523 > U533 > mark1
proper1 > U741 > tt > U543 > isNeList1 > mark1
proper1 > U741 > tt > U552 > mark1
proper1 > U741 > tt > U622 > mark1
proper1 > U741 > tt > U822 > mark1
proper1 > U741 > ok > U112 > U122 > mark1
proper1 > U741 > ok > U223 > U233 > mark1
proper1 > U741 > ok > U252 > mark1
proper1 > U741 > ok > U322 > mark1
proper1 > U741 > ok > U331 > mark1
proper1 > U741 > ok > U413 > mark1
proper1 > U741 > ok > U433 > mark1
proper1 > U741 > ok > U452 > mark1
proper1 > U741 > ok > U523 > U533 > mark1
proper1 > U741 > ok > U543 > isNeList1 > mark1
proper1 > U741 > ok > U552 > mark1
proper1 > U741 > ok > U622 > mark1
proper1 > U741 > ok > U812 > mark1
proper1 > U741 > ok > U822 > mark1
proper1 > U741 > ok > U911 > mark1
proper1 > _2 > ok > U112 > U122 > mark1
proper1 > _2 > ok > U223 > U233 > mark1
proper1 > _2 > ok > U252 > mark1
proper1 > _2 > ok > U322 > mark1
proper1 > _2 > ok > U331 > mark1
proper1 > _2 > ok > U413 > mark1
proper1 > _2 > ok > U433 > mark1
proper1 > _2 > ok > U452 > mark1
proper1 > _2 > ok > U523 > U533 > mark1
proper1 > _2 > ok > U543 > isNeList1 > mark1
proper1 > _2 > ok > U552 > mark1
proper1 > _2 > ok > U622 > mark1
proper1 > _2 > ok > U812 > mark1
proper1 > _2 > ok > U822 > mark1
proper1 > _2 > ok > U911 > mark1
proper1 > nil > mark1
proper1 > isPalListKind > tt > U122 > mark1
proper1 > isPalListKind > tt > U223 > U233 > mark1
proper1 > isPalListKind > tt > U252 > mark1
proper1 > isPalListKind > tt > U322 > mark1
proper1 > isPalListKind > tt > U331 > mark1
proper1 > isPalListKind > tt > U433 > mark1
proper1 > isPalListKind > tt > U452 > mark1
proper1 > isPalListKind > tt > U523 > U533 > mark1
proper1 > isPalListKind > tt > U543 > isNeList1 > mark1
proper1 > isPalListKind > tt > U552 > mark1
proper1 > isPalListKind > tt > U622 > mark1
proper1 > isPalListKind > tt > U822 > mark1
proper1 > isPalListKind > ok > U112 > U122 > mark1
proper1 > isPalListKind > ok > U223 > U233 > mark1
proper1 > isPalListKind > ok > U252 > mark1
proper1 > isPalListKind > ok > U322 > mark1
proper1 > isPalListKind > ok > U331 > mark1
proper1 > isPalListKind > ok > U413 > mark1
proper1 > isPalListKind > ok > U433 > mark1
proper1 > isPalListKind > ok > U452 > mark1
proper1 > isPalListKind > ok > U523 > U533 > mark1
proper1 > isPalListKind > ok > U543 > isNeList1 > mark1
proper1 > isPalListKind > ok > U552 > mark1
proper1 > isPalListKind > ok > U622 > mark1
proper1 > isPalListKind > ok > U812 > mark1
proper1 > isPalListKind > ok > U822 > mark1
proper1 > isPalListKind > ok > U911 > mark1
proper1 > U213 > ok > U112 > U122 > mark1
proper1 > U213 > ok > U223 > U233 > mark1
proper1 > U213 > ok > U252 > mark1
proper1 > U213 > ok > U322 > mark1
proper1 > U213 > ok > U331 > mark1
proper1 > U213 > ok > U413 > mark1
proper1 > U213 > ok > U433 > mark1
proper1 > U213 > ok > U452 > mark1
proper1 > U213 > ok > U523 > U533 > mark1
proper1 > U213 > ok > U543 > isNeList1 > mark1
proper1 > U213 > ok > U552 > mark1
proper1 > U213 > ok > U622 > mark1
proper1 > U213 > ok > U812 > mark1
proper1 > U213 > ok > U822 > mark1
proper1 > U213 > ok > U911 > mark1
proper1 > U243 > ok > U112 > U122 > mark1
proper1 > U243 > ok > U223 > U233 > mark1
proper1 > U243 > ok > U252 > mark1
proper1 > U243 > ok > U322 > mark1
proper1 > U243 > ok > U331 > mark1
proper1 > U243 > ok > U413 > mark1
proper1 > U243 > ok > U433 > mark1
proper1 > U243 > ok > U452 > mark1
proper1 > U243 > ok > U523 > U533 > mark1
proper1 > U243 > ok > U543 > isNeList1 > mark1
proper1 > U243 > ok > U552 > mark1
proper1 > U243 > ok > U622 > mark1
proper1 > U243 > ok > U812 > mark1
proper1 > U243 > ok > U822 > mark1
proper1 > U243 > ok > U911 > mark1
proper1 > U261 > tt > U122 > mark1
proper1 > U261 > tt > U223 > U233 > mark1
proper1 > U261 > tt > U252 > mark1
proper1 > U261 > tt > U322 > mark1
proper1 > U261 > tt > U331 > mark1
proper1 > U261 > tt > U433 > mark1
proper1 > U261 > tt > U452 > mark1
proper1 > U261 > tt > U523 > U533 > mark1
proper1 > U261 > tt > U543 > isNeList1 > mark1
proper1 > U261 > tt > U552 > mark1
proper1 > U261 > tt > U622 > mark1
proper1 > U261 > tt > U822 > mark1
proper1 > U261 > ok > U112 > U122 > mark1
proper1 > U261 > ok > U223 > U233 > mark1
proper1 > U261 > ok > U252 > mark1
proper1 > U261 > ok > U322 > mark1
proper1 > U261 > ok > U331 > mark1
proper1 > U261 > ok > U413 > mark1
proper1 > U261 > ok > U433 > mark1
proper1 > U261 > ok > U452 > mark1
proper1 > U261 > ok > U523 > U533 > mark1
proper1 > U261 > ok > U543 > isNeList1 > mark1
proper1 > U261 > ok > U552 > mark1
proper1 > U261 > ok > U622 > mark1
proper1 > U261 > ok > U812 > mark1
proper1 > U261 > ok > U822 > mark1
proper1 > U261 > ok > U911 > mark1
proper1 > U312 > ok > U112 > U122 > mark1
proper1 > U312 > ok > U223 > U233 > mark1
proper1 > U312 > ok > U252 > mark1
proper1 > U312 > ok > U322 > mark1
proper1 > U312 > ok > U331 > mark1
proper1 > U312 > ok > U413 > mark1
proper1 > U312 > ok > U433 > mark1
proper1 > U312 > ok > U452 > mark1
proper1 > U312 > ok > U523 > U533 > mark1
proper1 > U312 > ok > U543 > isNeList1 > mark1
proper1 > U312 > ok > U552 > mark1
proper1 > U312 > ok > U622 > mark1
proper1 > U312 > ok > U812 > mark1
proper1 > U312 > ok > U822 > mark1
proper1 > U312 > ok > U911 > mark1
proper1 > isQid1 > tt > U122 > mark1
proper1 > isQid1 > tt > U223 > U233 > mark1
proper1 > isQid1 > tt > U252 > mark1
proper1 > isQid1 > tt > U322 > mark1
proper1 > isQid1 > tt > U331 > mark1
proper1 > isQid1 > tt > U433 > mark1
proper1 > isQid1 > tt > U452 > mark1
proper1 > isQid1 > tt > U523 > U533 > mark1
proper1 > isQid1 > tt > U543 > isNeList1 > mark1
proper1 > isQid1 > tt > U552 > mark1
proper1 > isQid1 > tt > U622 > mark1
proper1 > isQid1 > tt > U822 > mark1
proper1 > isQid1 > ok > U112 > U122 > mark1
proper1 > isQid1 > ok > U223 > U233 > mark1
proper1 > isQid1 > ok > U252 > mark1
proper1 > isQid1 > ok > U322 > mark1
proper1 > isQid1 > ok > U331 > mark1
proper1 > isQid1 > ok > U413 > mark1
proper1 > isQid1 > ok > U433 > mark1
proper1 > isQid1 > ok > U452 > mark1
proper1 > isQid1 > ok > U523 > U533 > mark1
proper1 > isQid1 > ok > U543 > isNeList1 > mark1
proper1 > isQid1 > ok > U552 > mark1
proper1 > isQid1 > ok > U622 > mark1
proper1 > isQid1 > ok > U812 > mark1
proper1 > isQid1 > ok > U822 > mark1
proper1 > isQid1 > ok > U911 > mark1
proper1 > U423 > ok > U112 > U122 > mark1
proper1 > U423 > ok > U223 > U233 > mark1
proper1 > U423 > ok > U252 > mark1
proper1 > U423 > ok > U322 > mark1
proper1 > U423 > ok > U331 > mark1
proper1 > U423 > ok > U413 > mark1
proper1 > U423 > ok > U433 > mark1
proper1 > U423 > ok > U452 > mark1
proper1 > U423 > ok > U523 > U533 > mark1
proper1 > U423 > ok > U543 > isNeList1 > mark1
proper1 > U423 > ok > U552 > mark1
proper1 > U423 > ok > U622 > mark1
proper1 > U423 > ok > U812 > mark1
proper1 > U423 > ok > U822 > mark1
proper1 > U423 > ok > U911 > mark1
proper1 > U443 > ok > U112 > U122 > mark1
proper1 > U443 > ok > U223 > U233 > mark1
proper1 > U443 > ok > U252 > mark1
proper1 > U443 > ok > U322 > mark1
proper1 > U443 > ok > U331 > mark1
proper1 > U443 > ok > U413 > mark1
proper1 > U443 > ok > U433 > mark1
proper1 > U443 > ok > U452 > mark1
proper1 > U443 > ok > U523 > U533 > mark1
proper1 > U443 > ok > U543 > isNeList1 > mark1
proper1 > U443 > ok > U552 > mark1
proper1 > U443 > ok > U622 > mark1
proper1 > U443 > ok > U812 > mark1
proper1 > U443 > ok > U822 > mark1
proper1 > U443 > ok > U911 > mark1
proper1 > U513 > ok > U112 > U122 > mark1
proper1 > U513 > ok > U223 > U233 > mark1
proper1 > U513 > ok > U252 > mark1
proper1 > U513 > ok > U322 > mark1
proper1 > U513 > ok > U331 > mark1
proper1 > U513 > ok > U413 > mark1
proper1 > U513 > ok > U433 > mark1
proper1 > U513 > ok > U452 > mark1
proper1 > U513 > ok > U523 > U533 > mark1
proper1 > U513 > ok > U543 > isNeList1 > mark1
proper1 > U513 > ok > U552 > mark1
proper1 > U513 > ok > U622 > mark1
proper1 > U513 > ok > U812 > mark1
proper1 > U513 > ok > U822 > mark1
proper1 > U513 > ok > U911 > mark1
proper1 > U561 > tt > U122 > mark1
proper1 > U561 > tt > U223 > U233 > mark1
proper1 > U561 > tt > U252 > mark1
proper1 > U561 > tt > U322 > mark1
proper1 > U561 > tt > U331 > mark1
proper1 > U561 > tt > U433 > mark1
proper1 > U561 > tt > U452 > mark1
proper1 > U561 > tt > U523 > U533 > mark1
proper1 > U561 > tt > U543 > isNeList1 > mark1
proper1 > U561 > tt > U552 > mark1
proper1 > U561 > tt > U622 > mark1
proper1 > U561 > tt > U822 > mark1
proper1 > U561 > ok > U112 > U122 > mark1
proper1 > U561 > ok > U223 > U233 > mark1
proper1 > U561 > ok > U252 > mark1
proper1 > U561 > ok > U322 > mark1
proper1 > U561 > ok > U331 > mark1
proper1 > U561 > ok > U413 > mark1
proper1 > U561 > ok > U433 > mark1
proper1 > U561 > ok > U452 > mark1
proper1 > U561 > ok > U523 > U533 > mark1
proper1 > U561 > ok > U543 > isNeList1 > mark1
proper1 > U561 > ok > U552 > mark1
proper1 > U561 > ok > U622 > mark1
proper1 > U561 > ok > U812 > mark1
proper1 > U561 > ok > U822 > mark1
proper1 > U561 > ok > U911 > mark1
proper1 > U612 > ok > U112 > U122 > mark1
proper1 > U612 > ok > U223 > U233 > mark1
proper1 > U612 > ok > U252 > mark1
proper1 > U612 > ok > U322 > mark1
proper1 > U612 > ok > U331 > mark1
proper1 > U612 > ok > U413 > mark1
proper1 > U612 > ok > U433 > mark1
proper1 > U612 > ok > U452 > mark1
proper1 > U612 > ok > U523 > U533 > mark1
proper1 > U612 > ok > U543 > isNeList1 > mark1
proper1 > U612 > ok > U552 > mark1
proper1 > U612 > ok > U622 > mark1
proper1 > U612 > ok > U812 > mark1
proper1 > U612 > ok > U822 > mark1
proper1 > U612 > ok > U911 > mark1
proper1 > U713 > ok > U112 > U122 > mark1
proper1 > U713 > ok > U223 > U233 > mark1
proper1 > U713 > ok > U252 > mark1
proper1 > U713 > ok > U322 > mark1
proper1 > U713 > ok > U331 > mark1
proper1 > U713 > ok > U413 > mark1
proper1 > U713 > ok > U433 > mark1
proper1 > U713 > ok > U452 > mark1
proper1 > U713 > ok > U523 > U533 > mark1
proper1 > U713 > ok > U543 > isNeList1 > mark1
proper1 > U713 > ok > U552 > mark1
proper1 > U713 > ok > U622 > mark1
proper1 > U713 > ok > U812 > mark1
proper1 > U713 > ok > U822 > mark1
proper1 > U713 > ok > U911 > mark1
proper1 > U722 > U732 > ok > U112 > U122 > mark1
proper1 > U722 > U732 > ok > U223 > U233 > mark1
proper1 > U722 > U732 > ok > U252 > mark1
proper1 > U722 > U732 > ok > U322 > mark1
proper1 > U722 > U732 > ok > U331 > mark1
proper1 > U722 > U732 > ok > U413 > mark1
proper1 > U722 > U732 > ok > U433 > mark1
proper1 > U722 > U732 > ok > U452 > mark1
proper1 > U722 > U732 > ok > U523 > U533 > mark1
proper1 > U722 > U732 > ok > U543 > isNeList1 > mark1
proper1 > U722 > U732 > ok > U552 > mark1
proper1 > U722 > U732 > ok > U622 > mark1
proper1 > U722 > U732 > ok > U812 > mark1
proper1 > U722 > U732 > ok > U822 > mark1
proper1 > U722 > U732 > ok > U911 > mark1
proper1 > isPal1 > tt > U122 > mark1
proper1 > isPal1 > tt > U223 > U233 > mark1
proper1 > isPal1 > tt > U252 > mark1
proper1 > isPal1 > tt > U322 > mark1
proper1 > isPal1 > tt > U331 > mark1
proper1 > isPal1 > tt > U433 > mark1
proper1 > isPal1 > tt > U452 > mark1
proper1 > isPal1 > tt > U523 > U533 > mark1
proper1 > isPal1 > tt > U543 > isNeList1 > mark1
proper1 > isPal1 > tt > U552 > mark1
proper1 > isPal1 > tt > U622 > mark1
proper1 > isPal1 > tt > U822 > mark1
proper1 > isPal1 > ok > U112 > U122 > mark1
proper1 > isPal1 > ok > U223 > U233 > mark1
proper1 > isPal1 > ok > U252 > mark1
proper1 > isPal1 > ok > U322 > mark1
proper1 > isPal1 > ok > U331 > mark1
proper1 > isPal1 > ok > U413 > mark1
proper1 > isPal1 > ok > U433 > mark1
proper1 > isPal1 > ok > U452 > mark1
proper1 > isPal1 > ok > U523 > U533 > mark1
proper1 > isPal1 > ok > U543 > isNeList1 > mark1
proper1 > isPal1 > ok > U552 > mark1
proper1 > isPal1 > ok > U622 > mark1
proper1 > isPal1 > ok > U812 > mark1
proper1 > isPal1 > ok > U822 > mark1
proper1 > isPal1 > ok > U911 > mark1
proper1 > a > mark1
proper1 > e > mark1
proper1 > i > mark1
proper1 > o > mark1
proper1 > u > mark1
top > active1 > U741 > tt > U122 > mark1
top > active1 > U741 > tt > U223 > U233 > mark1
top > active1 > U741 > tt > U252 > mark1
top > active1 > U741 > tt > U322 > mark1
top > active1 > U741 > tt > U331 > mark1
top > active1 > U741 > tt > U433 > mark1
top > active1 > U741 > tt > U452 > mark1
top > active1 > U741 > tt > U523 > U533 > mark1
top > active1 > U741 > tt > U543 > isNeList1 > mark1
top > active1 > U741 > tt > U552 > mark1
top > active1 > U741 > tt > U622 > mark1
top > active1 > U741 > tt > U822 > mark1
top > active1 > U741 > ok > U112 > U122 > mark1
top > active1 > U741 > ok > U223 > U233 > mark1
top > active1 > U741 > ok > U252 > mark1
top > active1 > U741 > ok > U322 > mark1
top > active1 > U741 > ok > U331 > mark1
top > active1 > U741 > ok > U413 > mark1
top > active1 > U741 > ok > U433 > mark1
top > active1 > U741 > ok > U452 > mark1
top > active1 > U741 > ok > U523 > U533 > mark1
top > active1 > U741 > ok > U543 > isNeList1 > mark1
top > active1 > U741 > ok > U552 > mark1
top > active1 > U741 > ok > U622 > mark1
top > active1 > U741 > ok > U812 > mark1
top > active1 > U741 > ok > U822 > mark1
top > active1 > U741 > ok > U911 > mark1
top > active1 > _2 > ok > U112 > U122 > mark1
top > active1 > _2 > ok > U223 > U233 > mark1
top > active1 > _2 > ok > U252 > mark1
top > active1 > _2 > ok > U322 > mark1
top > active1 > _2 > ok > U331 > mark1
top > active1 > _2 > ok > U413 > mark1
top > active1 > _2 > ok > U433 > mark1
top > active1 > _2 > ok > U452 > mark1
top > active1 > _2 > ok > U523 > U533 > mark1
top > active1 > _2 > ok > U543 > isNeList1 > mark1
top > active1 > _2 > ok > U552 > mark1
top > active1 > _2 > ok > U622 > mark1
top > active1 > _2 > ok > U812 > mark1
top > active1 > _2 > ok > U822 > mark1
top > active1 > _2 > ok > U911 > mark1
top > active1 > isPalListKind > tt > U122 > mark1
top > active1 > isPalListKind > tt > U223 > U233 > mark1
top > active1 > isPalListKind > tt > U252 > mark1
top > active1 > isPalListKind > tt > U322 > mark1
top > active1 > isPalListKind > tt > U331 > mark1
top > active1 > isPalListKind > tt > U433 > mark1
top > active1 > isPalListKind > tt > U452 > mark1
top > active1 > isPalListKind > tt > U523 > U533 > mark1
top > active1 > isPalListKind > tt > U543 > isNeList1 > mark1
top > active1 > isPalListKind > tt > U552 > mark1
top > active1 > isPalListKind > tt > U622 > mark1
top > active1 > isPalListKind > tt > U822 > mark1
top > active1 > isPalListKind > ok > U112 > U122 > mark1
top > active1 > isPalListKind > ok > U223 > U233 > mark1
top > active1 > isPalListKind > ok > U252 > mark1
top > active1 > isPalListKind > ok > U322 > mark1
top > active1 > isPalListKind > ok > U331 > mark1
top > active1 > isPalListKind > ok > U413 > mark1
top > active1 > isPalListKind > ok > U433 > mark1
top > active1 > isPalListKind > ok > U452 > mark1
top > active1 > isPalListKind > ok > U523 > U533 > mark1
top > active1 > isPalListKind > ok > U543 > isNeList1 > mark1
top > active1 > isPalListKind > ok > U552 > mark1
top > active1 > isPalListKind > ok > U622 > mark1
top > active1 > isPalListKind > ok > U812 > mark1
top > active1 > isPalListKind > ok > U822 > mark1
top > active1 > isPalListKind > ok > U911 > mark1
top > active1 > U213 > ok > U112 > U122 > mark1
top > active1 > U213 > ok > U223 > U233 > mark1
top > active1 > U213 > ok > U252 > mark1
top > active1 > U213 > ok > U322 > mark1
top > active1 > U213 > ok > U331 > mark1
top > active1 > U213 > ok > U413 > mark1
top > active1 > U213 > ok > U433 > mark1
top > active1 > U213 > ok > U452 > mark1
top > active1 > U213 > ok > U523 > U533 > mark1
top > active1 > U213 > ok > U543 > isNeList1 > mark1
top > active1 > U213 > ok > U552 > mark1
top > active1 > U213 > ok > U622 > mark1
top > active1 > U213 > ok > U812 > mark1
top > active1 > U213 > ok > U822 > mark1
top > active1 > U213 > ok > U911 > mark1
top > active1 > U243 > ok > U112 > U122 > mark1
top > active1 > U243 > ok > U223 > U233 > mark1
top > active1 > U243 > ok > U252 > mark1
top > active1 > U243 > ok > U322 > mark1
top > active1 > U243 > ok > U331 > mark1
top > active1 > U243 > ok > U413 > mark1
top > active1 > U243 > ok > U433 > mark1
top > active1 > U243 > ok > U452 > mark1
top > active1 > U243 > ok > U523 > U533 > mark1
top > active1 > U243 > ok > U543 > isNeList1 > mark1
top > active1 > U243 > ok > U552 > mark1
top > active1 > U243 > ok > U622 > mark1
top > active1 > U243 > ok > U812 > mark1
top > active1 > U243 > ok > U822 > mark1
top > active1 > U243 > ok > U911 > mark1
top > active1 > U261 > tt > U122 > mark1
top > active1 > U261 > tt > U223 > U233 > mark1
top > active1 > U261 > tt > U252 > mark1
top > active1 > U261 > tt > U322 > mark1
top > active1 > U261 > tt > U331 > mark1
top > active1 > U261 > tt > U433 > mark1
top > active1 > U261 > tt > U452 > mark1
top > active1 > U261 > tt > U523 > U533 > mark1
top > active1 > U261 > tt > U543 > isNeList1 > mark1
top > active1 > U261 > tt > U552 > mark1
top > active1 > U261 > tt > U622 > mark1
top > active1 > U261 > tt > U822 > mark1
top > active1 > U261 > ok > U112 > U122 > mark1
top > active1 > U261 > ok > U223 > U233 > mark1
top > active1 > U261 > ok > U252 > mark1
top > active1 > U261 > ok > U322 > mark1
top > active1 > U261 > ok > U331 > mark1
top > active1 > U261 > ok > U413 > mark1
top > active1 > U261 > ok > U433 > mark1
top > active1 > U261 > ok > U452 > mark1
top > active1 > U261 > ok > U523 > U533 > mark1
top > active1 > U261 > ok > U543 > isNeList1 > mark1
top > active1 > U261 > ok > U552 > mark1
top > active1 > U261 > ok > U622 > mark1
top > active1 > U261 > ok > U812 > mark1
top > active1 > U261 > ok > U822 > mark1
top > active1 > U261 > ok > U911 > mark1
top > active1 > U312 > ok > U112 > U122 > mark1
top > active1 > U312 > ok > U223 > U233 > mark1
top > active1 > U312 > ok > U252 > mark1
top > active1 > U312 > ok > U322 > mark1
top > active1 > U312 > ok > U331 > mark1
top > active1 > U312 > ok > U413 > mark1
top > active1 > U312 > ok > U433 > mark1
top > active1 > U312 > ok > U452 > mark1
top > active1 > U312 > ok > U523 > U533 > mark1
top > active1 > U312 > ok > U543 > isNeList1 > mark1
top > active1 > U312 > ok > U552 > mark1
top > active1 > U312 > ok > U622 > mark1
top > active1 > U312 > ok > U812 > mark1
top > active1 > U312 > ok > U822 > mark1
top > active1 > U312 > ok > U911 > mark1
top > active1 > isQid1 > tt > U122 > mark1
top > active1 > isQid1 > tt > U223 > U233 > mark1
top > active1 > isQid1 > tt > U252 > mark1
top > active1 > isQid1 > tt > U322 > mark1
top > active1 > isQid1 > tt > U331 > mark1
top > active1 > isQid1 > tt > U433 > mark1
top > active1 > isQid1 > tt > U452 > mark1
top > active1 > isQid1 > tt > U523 > U533 > mark1
top > active1 > isQid1 > tt > U543 > isNeList1 > mark1
top > active1 > isQid1 > tt > U552 > mark1
top > active1 > isQid1 > tt > U622 > mark1
top > active1 > isQid1 > tt > U822 > mark1
top > active1 > isQid1 > ok > U112 > U122 > mark1
top > active1 > isQid1 > ok > U223 > U233 > mark1
top > active1 > isQid1 > ok > U252 > mark1
top > active1 > isQid1 > ok > U322 > mark1
top > active1 > isQid1 > ok > U331 > mark1
top > active1 > isQid1 > ok > U413 > mark1
top > active1 > isQid1 > ok > U433 > mark1
top > active1 > isQid1 > ok > U452 > mark1
top > active1 > isQid1 > ok > U523 > U533 > mark1
top > active1 > isQid1 > ok > U543 > isNeList1 > mark1
top > active1 > isQid1 > ok > U552 > mark1
top > active1 > isQid1 > ok > U622 > mark1
top > active1 > isQid1 > ok > U812 > mark1
top > active1 > isQid1 > ok > U822 > mark1
top > active1 > isQid1 > ok > U911 > mark1
top > active1 > U423 > ok > U112 > U122 > mark1
top > active1 > U423 > ok > U223 > U233 > mark1
top > active1 > U423 > ok > U252 > mark1
top > active1 > U423 > ok > U322 > mark1
top > active1 > U423 > ok > U331 > mark1
top > active1 > U423 > ok > U413 > mark1
top > active1 > U423 > ok > U433 > mark1
top > active1 > U423 > ok > U452 > mark1
top > active1 > U423 > ok > U523 > U533 > mark1
top > active1 > U423 > ok > U543 > isNeList1 > mark1
top > active1 > U423 > ok > U552 > mark1
top > active1 > U423 > ok > U622 > mark1
top > active1 > U423 > ok > U812 > mark1
top > active1 > U423 > ok > U822 > mark1
top > active1 > U423 > ok > U911 > mark1
top > active1 > U443 > ok > U112 > U122 > mark1
top > active1 > U443 > ok > U223 > U233 > mark1
top > active1 > U443 > ok > U252 > mark1
top > active1 > U443 > ok > U322 > mark1
top > active1 > U443 > ok > U331 > mark1
top > active1 > U443 > ok > U413 > mark1
top > active1 > U443 > ok > U433 > mark1
top > active1 > U443 > ok > U452 > mark1
top > active1 > U443 > ok > U523 > U533 > mark1
top > active1 > U443 > ok > U543 > isNeList1 > mark1
top > active1 > U443 > ok > U552 > mark1
top > active1 > U443 > ok > U622 > mark1
top > active1 > U443 > ok > U812 > mark1
top > active1 > U443 > ok > U822 > mark1
top > active1 > U443 > ok > U911 > mark1
top > active1 > U513 > ok > U112 > U122 > mark1
top > active1 > U513 > ok > U223 > U233 > mark1
top > active1 > U513 > ok > U252 > mark1
top > active1 > U513 > ok > U322 > mark1
top > active1 > U513 > ok > U331 > mark1
top > active1 > U513 > ok > U413 > mark1
top > active1 > U513 > ok > U433 > mark1
top > active1 > U513 > ok > U452 > mark1
top > active1 > U513 > ok > U523 > U533 > mark1
top > active1 > U513 > ok > U543 > isNeList1 > mark1
top > active1 > U513 > ok > U552 > mark1
top > active1 > U513 > ok > U622 > mark1
top > active1 > U513 > ok > U812 > mark1
top > active1 > U513 > ok > U822 > mark1
top > active1 > U513 > ok > U911 > mark1
top > active1 > U561 > tt > U122 > mark1
top > active1 > U561 > tt > U223 > U233 > mark1
top > active1 > U561 > tt > U252 > mark1
top > active1 > U561 > tt > U322 > mark1
top > active1 > U561 > tt > U331 > mark1
top > active1 > U561 > tt > U433 > mark1
top > active1 > U561 > tt > U452 > mark1
top > active1 > U561 > tt > U523 > U533 > mark1
top > active1 > U561 > tt > U543 > isNeList1 > mark1
top > active1 > U561 > tt > U552 > mark1
top > active1 > U561 > tt > U622 > mark1
top > active1 > U561 > tt > U822 > mark1
top > active1 > U561 > ok > U112 > U122 > mark1
top > active1 > U561 > ok > U223 > U233 > mark1
top > active1 > U561 > ok > U252 > mark1
top > active1 > U561 > ok > U322 > mark1
top > active1 > U561 > ok > U331 > mark1
top > active1 > U561 > ok > U413 > mark1
top > active1 > U561 > ok > U433 > mark1
top > active1 > U561 > ok > U452 > mark1
top > active1 > U561 > ok > U523 > U533 > mark1
top > active1 > U561 > ok > U543 > isNeList1 > mark1
top > active1 > U561 > ok > U552 > mark1
top > active1 > U561 > ok > U622 > mark1
top > active1 > U561 > ok > U812 > mark1
top > active1 > U561 > ok > U822 > mark1
top > active1 > U561 > ok > U911 > mark1
top > active1 > U612 > ok > U112 > U122 > mark1
top > active1 > U612 > ok > U223 > U233 > mark1
top > active1 > U612 > ok > U252 > mark1
top > active1 > U612 > ok > U322 > mark1
top > active1 > U612 > ok > U331 > mark1
top > active1 > U612 > ok > U413 > mark1
top > active1 > U612 > ok > U433 > mark1
top > active1 > U612 > ok > U452 > mark1
top > active1 > U612 > ok > U523 > U533 > mark1
top > active1 > U612 > ok > U543 > isNeList1 > mark1
top > active1 > U612 > ok > U552 > mark1
top > active1 > U612 > ok > U622 > mark1
top > active1 > U612 > ok > U812 > mark1
top > active1 > U612 > ok > U822 > mark1
top > active1 > U612 > ok > U911 > mark1
top > active1 > U713 > ok > U112 > U122 > mark1
top > active1 > U713 > ok > U223 > U233 > mark1
top > active1 > U713 > ok > U252 > mark1
top > active1 > U713 > ok > U322 > mark1
top > active1 > U713 > ok > U331 > mark1
top > active1 > U713 > ok > U413 > mark1
top > active1 > U713 > ok > U433 > mark1
top > active1 > U713 > ok > U452 > mark1
top > active1 > U713 > ok > U523 > U533 > mark1
top > active1 > U713 > ok > U543 > isNeList1 > mark1
top > active1 > U713 > ok > U552 > mark1
top > active1 > U713 > ok > U622 > mark1
top > active1 > U713 > ok > U812 > mark1
top > active1 > U713 > ok > U822 > mark1
top > active1 > U713 > ok > U911 > mark1
top > active1 > U722 > U732 > ok > U112 > U122 > mark1
top > active1 > U722 > U732 > ok > U223 > U233 > mark1
top > active1 > U722 > U732 > ok > U252 > mark1
top > active1 > U722 > U732 > ok > U322 > mark1
top > active1 > U722 > U732 > ok > U331 > mark1
top > active1 > U722 > U732 > ok > U413 > mark1
top > active1 > U722 > U732 > ok > U433 > mark1
top > active1 > U722 > U732 > ok > U452 > mark1
top > active1 > U722 > U732 > ok > U523 > U533 > mark1
top > active1 > U722 > U732 > ok > U543 > isNeList1 > mark1
top > active1 > U722 > U732 > ok > U552 > mark1
top > active1 > U722 > U732 > ok > U622 > mark1
top > active1 > U722 > U732 > ok > U812 > mark1
top > active1 > U722 > U732 > ok > U822 > mark1
top > active1 > U722 > U732 > ok > U911 > mark1
top > active1 > isPal1 > tt > U122 > mark1
top > active1 > isPal1 > tt > U223 > U233 > mark1
top > active1 > isPal1 > tt > U252 > mark1
top > active1 > isPal1 > tt > U322 > mark1
top > active1 > isPal1 > tt > U331 > mark1
top > active1 > isPal1 > tt > U433 > mark1
top > active1 > isPal1 > tt > U452 > mark1
top > active1 > isPal1 > tt > U523 > U533 > mark1
top > active1 > isPal1 > tt > U543 > isNeList1 > mark1
top > active1 > isPal1 > tt > U552 > mark1
top > active1 > isPal1 > tt > U622 > mark1
top > active1 > isPal1 > tt > U822 > mark1
top > active1 > isPal1 > ok > U112 > U122 > mark1
top > active1 > isPal1 > ok > U223 > U233 > mark1
top > active1 > isPal1 > ok > U252 > mark1
top > active1 > isPal1 > ok > U322 > mark1
top > active1 > isPal1 > ok > U331 > mark1
top > active1 > isPal1 > ok > U413 > mark1
top > active1 > isPal1 > ok > U433 > mark1
top > active1 > isPal1 > ok > U452 > mark1
top > active1 > isPal1 > ok > U523 > U533 > mark1
top > active1 > isPal1 > ok > U543 > isNeList1 > mark1
top > active1 > isPal1 > ok > U552 > mark1
top > active1 > isPal1 > ok > U622 > mark1
top > active1 > isPal1 > ok > U812 > mark1
top > active1 > isPal1 > ok > U822 > mark1
top > active1 > isPal1 > ok > U911 > mark1

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

(315) Obligation:

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

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

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

(316) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
active1 > U831 > mark1
active1 > U831 > tt > ok > isNePal1
active1 > _2 > U411 > mark1
active1 > _2 > U411 > ok > isNePal1
active1 > _2 > U713 > mark1
active1 > _2 > U713 > ok > isNePal1
active1 > isPalListKind > mark1
active1 > isPalListKind > tt > ok > isNePal1
active1 > isNeList > U411 > mark1
active1 > isNeList > U411 > ok > isNePal1
active1 > U211 > U221 > U231 > mark1
active1 > U211 > U221 > U231 > ok > isNePal1
active1 > U331 > mark1
active1 > U331 > tt > ok > isNePal1
active1 > isQid > mark1
active1 > isQid > tt > ok > isNePal1
active1 > U421 > mark1
active1 > U421 > ok > isNePal1
active1 > U451 > mark1
active1 > U451 > ok > isNePal1
active1 > U521 > mark1
active1 > U521 > ok > isNePal1
active1 > U531 > mark1
active1 > U531 > ok > isNePal1
active1 > U541 > mark1
active1 > U541 > ok > isNePal1
active1 > U551 > isList > tt > ok > isNePal1
active1 > U551 > U561 > mark1
active1 > U551 > U561 > tt > ok > isNePal1
active1 > U612 > mark1
active1 > U612 > ok > isNePal1
active1 > U622 > mark1
active1 > U622 > ok > isNePal1
active1 > U722 > mark1
active1 > U722 > ok > isNePal1
active1 > isPal1 > tt > ok > isNePal1
active1 > isPal1 > U812 > mark1
active1 > isPal1 > U812 > ok > isNePal1
active1 > U741 > mark1
active1 > U741 > tt > ok > isNePal1
active1 > U822 > mark1
active1 > U822 > ok > isNePal1
active1 > U921 > mark1
active1 > U921 > tt > ok > isNePal1
nil > ok > isNePal1
a > tt > ok > isNePal1
e > mark1
e > tt > ok > isNePal1
i > ok > isNePal1
o > mark1
o > tt > ok > isNePal1
u > mark1
u > tt > ok > isNePal1

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

(317) Obligation:

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

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

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

(318) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
active1 > U131 > tt > isNeList > ok > U311 > mark1
active1 > U131 > tt > isNeList > ok > U321 > mark1
active1 > U131 > tt > isNeList > ok > U451 > mark1
active1 > U131 > tt > isNeList > ok > U521 > mark1
active1 > U131 > tt > isNeList > ok > U541 > mark1
active1 > U131 > tt > isNeList > ok > U612 > mark1
active1 > U131 > tt > isNeList > ok > U722 > mark1
active1 > U131 > tt > isNeList > ok > U822 > mark1
active1 > U131 > tt > isNeList > ok > isNePal1 > mark1
active1 > U131 > tt > U441 > ok > U311 > mark1
active1 > U131 > tt > U441 > ok > U321 > mark1
active1 > U131 > tt > U441 > ok > U451 > mark1
active1 > U131 > tt > U441 > ok > U521 > mark1
active1 > U131 > tt > U441 > ok > U541 > mark1
active1 > U131 > tt > U441 > ok > U612 > mark1
active1 > U131 > tt > U441 > ok > U722 > mark1
active1 > U131 > tt > U441 > ok > U822 > mark1
active1 > U131 > tt > U441 > ok > isNePal1 > mark1
active1 > U131 > tt > U561 > ok > U311 > mark1
active1 > U131 > tt > U561 > ok > U321 > mark1
active1 > U131 > tt > U561 > ok > U451 > mark1
active1 > U131 > tt > U561 > ok > U521 > mark1
active1 > U131 > tt > U561 > ok > U541 > mark1
active1 > U131 > tt > U561 > ok > U612 > mark1
active1 > U131 > tt > U561 > ok > U722 > mark1
active1 > U131 > tt > U561 > ok > U822 > mark1
active1 > U131 > tt > U561 > ok > isNePal1 > mark1
active1 > U131 > tt > U732 > U741 > ok > U311 > mark1
active1 > U131 > tt > U732 > U741 > ok > U321 > mark1
active1 > U131 > tt > U732 > U741 > ok > U451 > mark1
active1 > U131 > tt > U732 > U741 > ok > U521 > mark1
active1 > U131 > tt > U732 > U741 > ok > U541 > mark1
active1 > U131 > tt > U732 > U741 > ok > U612 > mark1
active1 > U131 > tt > U732 > U741 > ok > U722 > mark1
active1 > U131 > tt > U732 > U741 > ok > U822 > mark1
active1 > U131 > tt > U732 > U741 > ok > isNePal1 > mark1
active1 > U131 > tt > isPal1 > ok > U311 > mark1
active1 > U131 > tt > isPal1 > ok > U321 > mark1
active1 > U131 > tt > isPal1 > ok > U451 > mark1
active1 > U131 > tt > isPal1 > ok > U521 > mark1
active1 > U131 > tt > isPal1 > ok > U541 > mark1
active1 > U131 > tt > isPal1 > ok > U612 > mark1
active1 > U131 > tt > isPal1 > ok > U722 > mark1
active1 > U131 > tt > isPal1 > ok > U822 > mark1
active1 > U131 > tt > isPal1 > ok > isNePal1 > mark1
active1 > _2 > U211 > ok > U311 > mark1
active1 > _2 > U211 > ok > U321 > mark1
active1 > _2 > U211 > ok > U451 > mark1
active1 > _2 > U211 > ok > U521 > mark1
active1 > _2 > U211 > ok > U541 > mark1
active1 > _2 > U211 > ok > U612 > mark1
active1 > _2 > U211 > ok > U722 > mark1
active1 > _2 > U211 > ok > U822 > mark1
active1 > _2 > U211 > ok > isNePal1 > mark1
active1 > _2 > U511 > ok > U311 > mark1
active1 > _2 > U511 > ok > U321 > mark1
active1 > _2 > U511 > ok > U451 > mark1
active1 > _2 > U511 > ok > U521 > mark1
active1 > _2 > U511 > ok > U541 > mark1
active1 > _2 > U511 > ok > U612 > mark1
active1 > _2 > U511 > ok > U722 > mark1
active1 > _2 > U511 > ok > U822 > mark1
active1 > _2 > U511 > ok > isNePal1 > mark1
active1 > _2 > U713 > ok > U311 > mark1
active1 > _2 > U713 > ok > U321 > mark1
active1 > _2 > U713 > ok > U451 > mark1
active1 > _2 > U713 > ok > U521 > mark1
active1 > _2 > U713 > ok > U541 > mark1
active1 > _2 > U713 > ok > U612 > mark1
active1 > _2 > U713 > ok > U722 > mark1
active1 > _2 > U713 > ok > U822 > mark1
active1 > _2 > U713 > ok > isNePal1 > mark1
active1 > _2 > U911 > ok > U311 > mark1
active1 > _2 > U911 > ok > U321 > mark1
active1 > _2 > U911 > ok > U451 > mark1
active1 > _2 > U911 > ok > U521 > mark1
active1 > _2 > U911 > ok > U541 > mark1
active1 > _2 > U911 > ok > U612 > mark1
active1 > _2 > U911 > ok > U722 > mark1
active1 > _2 > U911 > ok > U822 > mark1
active1 > _2 > U911 > ok > isNePal1 > mark1
active1 > isPalListKind > tt > isNeList > ok > U311 > mark1
active1 > isPalListKind > tt > isNeList > ok > U321 > mark1
active1 > isPalListKind > tt > isNeList > ok > U451 > mark1
active1 > isPalListKind > tt > isNeList > ok > U521 > mark1
active1 > isPalListKind > tt > isNeList > ok > U541 > mark1
active1 > isPalListKind > tt > isNeList > ok > U612 > mark1
active1 > isPalListKind > tt > isNeList > ok > U722 > mark1
active1 > isPalListKind > tt > isNeList > ok > U822 > mark1
active1 > isPalListKind > tt > isNeList > ok > isNePal1 > mark1
active1 > isPalListKind > tt > U441 > ok > U311 > mark1
active1 > isPalListKind > tt > U441 > ok > U321 > mark1
active1 > isPalListKind > tt > U441 > ok > U451 > mark1
active1 > isPalListKind > tt > U441 > ok > U521 > mark1
active1 > isPalListKind > tt > U441 > ok > U541 > mark1
active1 > isPalListKind > tt > U441 > ok > U612 > mark1
active1 > isPalListKind > tt > U441 > ok > U722 > mark1
active1 > isPalListKind > tt > U441 > ok > U822 > mark1
active1 > isPalListKind > tt > U441 > ok > isNePal1 > mark1
active1 > isPalListKind > tt > U561 > ok > U311 > mark1
active1 > isPalListKind > tt > U561 > ok > U321 > mark1
active1 > isPalListKind > tt > U561 > ok > U451 > mark1
active1 > isPalListKind > tt > U561 > ok > U521 > mark1
active1 > isPalListKind > tt > U561 > ok > U541 > mark1
active1 > isPalListKind > tt > U561 > ok > U612 > mark1
active1 > isPalListKind > tt > U561 > ok > U722 > mark1
active1 > isPalListKind > tt > U561 > ok > U822 > mark1
active1 > isPalListKind > tt > U561 > ok > isNePal1 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U311 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U321 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U451 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U521 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U541 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U612 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U722 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > U822 > mark1
active1 > isPalListKind > tt > U732 > U741 > ok > isNePal1 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U311 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U321 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U451 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U521 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U541 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U612 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U722 > mark1
active1 > isPalListKind > tt > isPal1 > ok > U822 > mark1
active1 > isPalListKind > tt > isPal1 > ok > isNePal1 > mark1
active1 > isPalListKind > U911 > ok > U311 > mark1
active1 > isPalListKind > U911 > ok > U321 > mark1
active1 > isPalListKind > U911 > ok > U451 > mark1
active1 > isPalListKind > U911 > ok > U521 > mark1
active1 > isPalListKind > U911 > ok > U541 > mark1
active1 > isPalListKind > U911 > ok > U612 > mark1
active1 > isPalListKind > U911 > ok > U722 > mark1
active1 > isPalListKind > U911 > ok > U822 > mark1
active1 > isPalListKind > U911 > ok > isNePal1 > mark1
active1 > U221 > ok > U311 > mark1
active1 > U221 > ok > U321 > mark1
active1 > U221 > ok > U451 > mark1
active1 > U221 > ok > U521 > mark1
active1 > U221 > ok > U541 > mark1
active1 > U221 > ok > U612 > mark1
active1 > U221 > ok > U722 > mark1
active1 > U221 > ok > U822 > mark1
active1 > U221 > ok > isNePal1 > mark1
active1 > isQid > tt > isNeList > ok > U311 > mark1
active1 > isQid > tt > isNeList > ok > U321 > mark1
active1 > isQid > tt > isNeList > ok > U451 > mark1
active1 > isQid > tt > isNeList > ok > U521 > mark1
active1 > isQid > tt > isNeList > ok > U541 > mark1
active1 > isQid > tt > isNeList > ok > U612 > mark1
active1 > isQid > tt > isNeList > ok > U722 > mark1
active1 > isQid > tt > isNeList > ok > U822 > mark1
active1 > isQid > tt > isNeList > ok > isNePal1 > mark1
active1 > isQid > tt > U441 > ok > U311 > mark1
active1 > isQid > tt > U441 > ok > U321 > mark1
active1 > isQid > tt > U441 > ok > U451 > mark1
active1 > isQid > tt > U441 > ok > U521 > mark1
active1 > isQid > tt > U441 > ok > U541 > mark1
active1 > isQid > tt > U441 > ok > U612 > mark1
active1 > isQid > tt > U441 > ok > U722 > mark1
active1 > isQid > tt > U441 > ok > U822 > mark1
active1 > isQid > tt > U441 > ok > isNePal1 > mark1
active1 > isQid > tt > U561 > ok > U311 > mark1
active1 > isQid > tt > U561 > ok > U321 > mark1
active1 > isQid > tt > U561 > ok > U451 > mark1
active1 > isQid > tt > U561 > ok > U521 > mark1
active1 > isQid > tt > U561 > ok > U541 > mark1
active1 > isQid > tt > U561 > ok > U612 > mark1
active1 > isQid > tt > U561 > ok > U722 > mark1
active1 > isQid > tt > U561 > ok > U822 > mark1
active1 > isQid > tt > U561 > ok > isNePal1 > mark1
active1 > isQid > tt > U732 > U741 > ok > U311 > mark1
active1 > isQid > tt > U732 > U741 > ok > U321 > mark1
active1 > isQid > tt > U732 > U741 > ok > U451 > mark1
active1 > isQid > tt > U732 > U741 > ok > U521 > mark1
active1 > isQid > tt > U732 > U741 > ok > U541 > mark1
active1 > isQid > tt > U732 > U741 > ok > U612 > mark1
active1 > isQid > tt > U732 > U741 > ok > U722 > mark1
active1 > isQid > tt > U732 > U741 > ok > U822 > mark1
active1 > isQid > tt > U732 > U741 > ok > isNePal1 > mark1
active1 > isQid > tt > isPal1 > ok > U311 > mark1
active1 > isQid > tt > isPal1 > ok > U321 > mark1
active1 > isQid > tt > isPal1 > ok > U451 > mark1
active1 > isQid > tt > isPal1 > ok > U521 > mark1
active1 > isQid > tt > isPal1 > ok > U541 > mark1
active1 > isQid > tt > isPal1 > ok > U612 > mark1
active1 > isQid > tt > isPal1 > ok > U722 > mark1
active1 > isQid > tt > isPal1 > ok > U822 > mark1
active1 > isQid > tt > isPal1 > ok > isNePal1 > mark1
active1 > U461 > tt > isNeList > ok > U311 > mark1
active1 > U461 > tt > isNeList > ok > U321 > mark1
active1 > U461 > tt > isNeList > ok > U451 > mark1
active1 > U461 > tt > isNeList > ok > U521 > mark1
active1 > U461 > tt > isNeList > ok > U541 > mark1
active1 > U461 > tt > isNeList > ok > U612 > mark1
active1 > U461 > tt > isNeList > ok > U722 > mark1
active1 > U461 > tt > isNeList > ok > U822 > mark1
active1 > U461 > tt > isNeList > ok > isNePal1 > mark1
active1 > U461 > tt > U441 > ok > U311 > mark1
active1 > U461 > tt > U441 > ok > U321 > mark1
active1 > U461 > tt > U441 > ok > U451 > mark1
active1 > U461 > tt > U441 > ok > U521 > mark1
active1 > U461 > tt > U441 > ok > U541 > mark1
active1 > U461 > tt > U441 > ok > U612 > mark1
active1 > U461 > tt > U441 > ok > U722 > mark1
active1 > U461 > tt > U441 > ok > U822 > mark1
active1 > U461 > tt > U441 > ok > isNePal1 > mark1
active1 > U461 > tt > U561 > ok > U311 > mark1
active1 > U461 > tt > U561 > ok > U321 > mark1
active1 > U461 > tt > U561 > ok > U451 > mark1
active1 > U461 > tt > U561 > ok > U521 > mark1
active1 > U461 > tt > U561 > ok > U541 > mark1
active1 > U461 > tt > U561 > ok > U612 > mark1
active1 > U461 > tt > U561 > ok > U722 > mark1
active1 > U461 > tt > U561 > ok > U822 > mark1
active1 > U461 > tt > U561 > ok > isNePal1 > mark1
active1 > U461 > tt > U732 > U741 > ok > U311 > mark1
active1 > U461 > tt > U732 > U741 > ok > U321 > mark1
active1 > U461 > tt > U732 > U741 > ok > U451 > mark1
active1 > U461 > tt > U732 > U741 > ok > U521 > mark1
active1 > U461 > tt > U732 > U741 > ok > U541 > mark1
active1 > U461 > tt > U732 > U741 > ok > U612 > mark1
active1 > U461 > tt > U732 > U741 > ok > U722 > mark1
active1 > U461 > tt > U732 > U741 > ok > U822 > mark1
active1 > U461 > tt > U732 > U741 > ok > isNePal1 > mark1
active1 > U461 > tt > isPal1 > ok > U311 > mark1
active1 > U461 > tt > isPal1 > ok > U321 > mark1
active1 > U461 > tt > isPal1 > ok > U451 > mark1
active1 > U461 > tt > isPal1 > ok > U521 > mark1
active1 > U461 > tt > isPal1 > ok > U541 > mark1
active1 > U461 > tt > isPal1 > ok > U612 > mark1
active1 > U461 > tt > isPal1 > ok > U722 > mark1
active1 > U461 > tt > isPal1 > ok > U822 > mark1
active1 > U461 > tt > isPal1 > ok > isNePal1 > mark1
active1 > U551 > isList > tt > isNeList > ok > U311 > mark1
active1 > U551 > isList > tt > isNeList > ok > U321 > mark1
active1 > U551 > isList > tt > isNeList > ok > U451 > mark1
active1 > U551 > isList > tt > isNeList > ok > U521 > mark1
active1 > U551 > isList > tt > isNeList > ok > U541 > mark1
active1 > U551 > isList > tt > isNeList > ok > U612 > mark1
active1 > U551 > isList > tt > isNeList > ok > U722 > mark1
active1 > U551 > isList > tt > isNeList > ok > U822 > mark1
active1 > U551 > isList > tt > isNeList > ok > isNePal1 > mark1
active1 > U551 > isList > tt > U441 > ok > U311 > mark1
active1 > U551 > isList > tt > U441 > ok > U321 > mark1
active1 > U551 > isList > tt > U441 > ok > U451 > mark1
active1 > U551 > isList > tt > U441 > ok > U521 > mark1
active1 > U551 > isList > tt > U441 > ok > U541 > mark1
active1 > U551 > isList > tt > U441 > ok > U612 > mark1
active1 > U551 > isList > tt > U441 > ok > U722 > mark1
active1 > U551 > isList > tt > U441 > ok > U822 > mark1
active1 > U551 > isList > tt > U441 > ok > isNePal1 > mark1
active1 > U551 > isList > tt > U561 > ok > U311 > mark1
active1 > U551 > isList > tt > U561 > ok > U321 > mark1
active1 > U551 > isList > tt > U561 > ok > U451 > mark1
active1 > U551 > isList > tt > U561 > ok > U521 > mark1
active1 > U551 > isList > tt > U561 > ok > U541 > mark1
active1 > U551 > isList > tt > U561 > ok > U612 > mark1
active1 > U551 > isList > tt > U561 > ok > U722 > mark1
active1 > U551 > isList > tt > U561 > ok > U822 > mark1
active1 > U551 > isList > tt > U561 > ok > isNePal1 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U311 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U321 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U451 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U521 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U541 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U612 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U722 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > U822 > mark1
active1 > U551 > isList > tt > U732 > U741 > ok > isNePal1 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U311 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U321 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U451 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U521 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U541 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U612 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U722 > mark1
active1 > U551 > isList > tt > isPal1 > ok > U822 > mark1
active1 > U551 > isList > tt > isPal1 > ok > isNePal1 > mark1
active1 > U551 > isList > U211 > ok > U311 > mark1
active1 > U551 > isList > U211 > ok > U321 > mark1
active1 > U551 > isList > U211 > ok > U451 > mark1
active1 > U551 > isList > U211 > ok > U521 > mark1
active1 > U551 > isList > U211 > ok > U541 > mark1
active1 > U551 > isList > U211 > ok > U612 > mark1
active1 > U551 > isList > U211 > ok > U722 > mark1
active1 > U551 > isList > U211 > ok > U822 > mark1
active1 > U551 > isList > U211 > ok > isNePal1 > mark1
active1 > U812 > ok > U311 > mark1
active1 > U812 > ok > U321 > mark1
active1 > U812 > ok > U451 > mark1
active1 > U812 > ok > U521 > mark1
active1 > U812 > ok > U541 > mark1
active1 > U812 > ok > U612 > mark1
active1 > U812 > ok > U722 > mark1
active1 > U812 > ok > U822 > mark1
active1 > U812 > ok > isNePal1 > mark1
proper1 > U131 > tt > isNeList > ok > U311 > mark1
proper1 > U131 > tt > isNeList > ok > U321 > mark1
proper1 > U131 > tt > isNeList > ok > U451 > mark1
proper1 > U131 > tt > isNeList > ok > U521 > mark1
proper1 > U131 > tt > isNeList > ok > U541 > mark1
proper1 > U131 > tt > isNeList > ok > U612 > mark1
proper1 > U131 > tt > isNeList > ok > U722 > mark1
proper1 > U131 > tt > isNeList > ok > U822 > mark1
proper1 > U131 > tt > isNeList > ok > isNePal1 > mark1
proper1 > U131 > tt > U441 > ok > U311 > mark1
proper1 > U131 > tt > U441 > ok > U321 > mark1
proper1 > U131 > tt > U441 > ok > U451 > mark1
proper1 > U131 > tt > U441 > ok > U521 > mark1
proper1 > U131 > tt > U441 > ok > U541 > mark1
proper1 > U131 > tt > U441 > ok > U612 > mark1
proper1 > U131 > tt > U441 > ok > U722 > mark1
proper1 > U131 > tt > U441 > ok > U822 > mark1
proper1 > U131 > tt > U441 > ok > isNePal1 > mark1
proper1 > U131 > tt > U561 > ok > U311 > mark1
proper1 > U131 > tt > U561 > ok > U321 > mark1
proper1 > U131 > tt > U561 > ok > U451 > mark1
proper1 > U131 > tt > U561 > ok > U521 > mark1
proper1 > U131 > tt > U561 > ok > U541 > mark1
proper1 > U131 > tt > U561 > ok > U612 > mark1
proper1 > U131 > tt > U561 > ok > U722 > mark1
proper1 > U131 > tt > U561 > ok > U822 > mark1
proper1 > U131 > tt > U561 > ok > isNePal1 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U311 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U321 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U451 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U521 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U541 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U612 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U722 > mark1
proper1 > U131 > tt > U732 > U741 > ok > U822 > mark1
proper1 > U131 > tt > U732 > U741 > ok > isNePal1 > mark1
proper1 > U131 > tt > isPal1 > ok > U311 > mark1
proper1 > U131 > tt > isPal1 > ok > U321 > mark1
proper1 > U131 > tt > isPal1 > ok > U451 > mark1
proper1 > U131 > tt > isPal1 > ok > U521 > mark1
proper1 > U131 > tt > isPal1 > ok > U541 > mark1
proper1 > U131 > tt > isPal1 > ok > U612 > mark1
proper1 > U131 > tt > isPal1 > ok > U722 > mark1
proper1 > U131 > tt > isPal1 > ok > U822 > mark1
proper1 > U131 > tt > isPal1 > ok > isNePal1 > mark1
proper1 > _2 > U211 > ok > U311 > mark1
proper1 > _2 > U211 > ok > U321 > mark1
proper1 > _2 > U211 > ok > U451 > mark1
proper1 > _2 > U211 > ok > U521 > mark1
proper1 > _2 > U211 > ok > U541 > mark1
proper1 > _2 > U211 > ok > U612 > mark1
proper1 > _2 > U211 > ok > U722 > mark1
proper1 > _2 > U211 > ok > U822 > mark1
proper1 > _2 > U211 > ok > isNePal1 > mark1
proper1 > _2 > U511 > ok > U311 > mark1
proper1 > _2 > U511 > ok > U321 > mark1
proper1 > _2 > U511 > ok > U451 > mark1
proper1 > _2 > U511 > ok > U521 > mark1
proper1 > _2 > U511 > ok > U541 > mark1
proper1 > _2 > U511 > ok > U612 > mark1
proper1 > _2 > U511 > ok > U722 > mark1
proper1 > _2 > U511 > ok > U822 > mark1
proper1 > _2 > U511 > ok > isNePal1 > mark1
proper1 > _2 > U713 > ok > U311 > mark1
proper1 > _2 > U713 > ok > U321 > mark1
proper1 > _2 > U713 > ok > U451 > mark1
proper1 > _2 > U713 > ok > U521 > mark1
proper1 > _2 > U713 > ok > U541 > mark1
proper1 > _2 > U713 > ok > U612 > mark1
proper1 > _2 > U713 > ok > U722 > mark1
proper1 > _2 > U713 > ok > U822 > mark1
proper1 > _2 > U713 > ok > isNePal1 > mark1
proper1 > _2 > U911 > ok > U311 > mark1
proper1 > _2 > U911 > ok > U321 > mark1
proper1 > _2 > U911 > ok > U451 > mark1
proper1 > _2 > U911 > ok > U521 > mark1
proper1 > _2 > U911 > ok > U541 > mark1
proper1 > _2 > U911 > ok > U612 > mark1
proper1 > _2 > U911 > ok > U722 > mark1
proper1 > _2 > U911 > ok > U822 > mark1
proper1 > _2 > U911 > ok > isNePal1 > mark1
proper1 > nil > mark1
proper1 > isPalListKind > tt > isNeList > ok > U311 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U321 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U451 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U521 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U541 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U612 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U722 > mark1
proper1 > isPalListKind > tt > isNeList > ok > U822 > mark1
proper1 > isPalListKind > tt > isNeList > ok > isNePal1 > mark1
proper1 > isPalListKind > tt > U441 > ok > U311 > mark1
proper1 > isPalListKind > tt > U441 > ok > U321 > mark1
proper1 > isPalListKind > tt > U441 > ok > U451 > mark1
proper1 > isPalListKind > tt > U441 > ok > U521 > mark1
proper1 > isPalListKind > tt > U441 > ok > U541 > mark1
proper1 > isPalListKind > tt > U441 > ok > U612 > mark1
proper1 > isPalListKind > tt > U441 > ok > U722 > mark1
proper1 > isPalListKind > tt > U441 > ok > U822 > mark1
proper1 > isPalListKind > tt > U441 > ok > isNePal1 > mark1
proper1 > isPalListKind > tt > U561 > ok > U311 > mark1
proper1 > isPalListKind > tt > U561 > ok > U321 > mark1
proper1 > isPalListKind > tt > U561 > ok > U451 > mark1
proper1 > isPalListKind > tt > U561 > ok > U521 > mark1
proper1 > isPalListKind > tt > U561 > ok > U541 > mark1
proper1 > isPalListKind > tt > U561 > ok > U612 > mark1
proper1 > isPalListKind > tt > U561 > ok > U722 > mark1
proper1 > isPalListKind > tt > U561 > ok > U822 > mark1
proper1 > isPalListKind > tt > U561 > ok > isNePal1 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U311 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U321 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U451 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U521 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U541 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U612 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U722 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > U822 > mark1
proper1 > isPalListKind > tt > U732 > U741 > ok > isNePal1 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U311 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U321 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U451 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U521 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U541 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U612 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U722 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > U822 > mark1
proper1 > isPalListKind > tt > isPal1 > ok > isNePal1 > mark1
proper1 > isPalListKind > U911 > ok > U311 > mark1
proper1 > isPalListKind > U911 > ok > U321 > mark1
proper1 > isPalListKind > U911 > ok > U451 > mark1
proper1 > isPalListKind > U911 > ok > U521 > mark1
proper1 > isPalListKind > U911 > ok > U541 > mark1
proper1 > isPalListKind > U911 > ok > U612 > mark1
proper1 > isPalListKind > U911 > ok > U722 > mark1
proper1 > isPalListKind > U911 > ok > U822 > mark1
proper1 > isPalListKind > U911 > ok > isNePal1 > mark1
proper1 > U221 > ok > U311 > mark1
proper1 > U221 > ok > U321 > mark1
proper1 > U221 > ok > U451 > mark1
proper1 > U221 > ok > U521 > mark1
proper1 > U221 > ok > U541 > mark1
proper1 > U221 > ok > U612 > mark1
proper1 > U221 > ok > U722 > mark1
proper1 > U221 > ok > U822 > mark1
proper1 > U221 > ok > isNePal1 > mark1
proper1 > isQid > tt > isNeList > ok > U311 > mark1
proper1 > isQid > tt > isNeList > ok > U321 > mark1
proper1 > isQid > tt > isNeList > ok > U451 > mark1
proper1 > isQid > tt > isNeList > ok > U521 > mark1
proper1 > isQid > tt > isNeList > ok > U541 > mark1
proper1 > isQid > tt > isNeList > ok > U612 > mark1
proper1 > isQid > tt > isNeList > ok > U722 > mark1
proper1 > isQid > tt > isNeList > ok > U822 > mark1
proper1 > isQid > tt > isNeList > ok > isNePal1 > mark1
proper1 > isQid > tt > U441 > ok > U311 > mark1
proper1 > isQid > tt > U441 > ok > U321 > mark1
proper1 > isQid > tt > U441 > ok > U451 > mark1
proper1 > isQid > tt > U441 > ok > U521 > mark1
proper1 > isQid > tt > U441 > ok > U541 > mark1
proper1 > isQid > tt > U441 > ok > U612 > mark1
proper1 > isQid > tt > U441 > ok > U722 > mark1
proper1 > isQid > tt > U441 > ok > U822 > mark1
proper1 > isQid > tt > U441 > ok > isNePal1 > mark1
proper1 > isQid > tt > U561 > ok > U311 > mark1
proper1 > isQid > tt > U561 > ok > U321 > mark1
proper1 > isQid > tt > U561 > ok > U451 > mark1
proper1 > isQid > tt > U561 > ok > U521 > mark1
proper1 > isQid > tt > U561 > ok > U541 > mark1
proper1 > isQid > tt > U561 > ok > U612 > mark1
proper1 > isQid > tt > U561 > ok > U722 > mark1
proper1 > isQid > tt > U561 > ok > U822 > mark1
proper1 > isQid > tt > U561 > ok > isNePal1 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U311 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U321 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U451 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U521 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U541 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U612 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U722 > mark1
proper1 > isQid > tt > U732 > U741 > ok > U822 > mark1
proper1 > isQid > tt > U732 > U741 > ok > isNePal1 > mark1
proper1 > isQid > tt > isPal1 > ok > U311 > mark1
proper1 > isQid > tt > isPal1 > ok > U321 > mark1
proper1 > isQid > tt > isPal1 > ok > U451 > mark1
proper1 > isQid > tt > isPal1 > ok > U521 > mark1
proper1 > isQid > tt > isPal1 > ok > U541 > mark1
proper1 > isQid > tt > isPal1 > ok > U612 > mark1
proper1 > isQid > tt > isPal1 > ok > U722 > mark1
proper1 > isQid > tt > isPal1 > ok > U822 > mark1
proper1 > isQid > tt > isPal1 > ok > isNePal1 > mark1
proper1 > U461 > tt > isNeList > ok > U311 > mark1
proper1 > U461 > tt > isNeList > ok > U321 > mark1
proper1 > U461 > tt > isNeList > ok > U451 > mark1
proper1 > U461 > tt > isNeList > ok > U521 > mark1
proper1 > U461 > tt > isNeList > ok > U541 > mark1
proper1 > U461 > tt > isNeList > ok > U612 > mark1
proper1 > U461 > tt > isNeList > ok > U722 > mark1
proper1 > U461 > tt > isNeList > ok > U822 > mark1
proper1 > U461 > tt > isNeList > ok > isNePal1 > mark1
proper1 > U461 > tt > U441 > ok > U311 > mark1
proper1 > U461 > tt > U441 > ok > U321 > mark1
proper1 > U461 > tt > U441 > ok > U451 > mark1
proper1 > U461 > tt > U441 > ok > U521 > mark1
proper1 > U461 > tt > U441 > ok > U541 > mark1
proper1 > U461 > tt > U441 > ok > U612 > mark1
proper1 > U461 > tt > U441 > ok > U722 > mark1
proper1 > U461 > tt > U441 > ok > U822 > mark1
proper1 > U461 > tt > U441 > ok > isNePal1 > mark1
proper1 > U461 > tt > U561 > ok > U311 > mark1
proper1 > U461 > tt > U561 > ok > U321 > mark1
proper1 > U461 > tt > U561 > ok > U451 > mark1
proper1 > U461 > tt > U561 > ok > U521 > mark1
proper1 > U461 > tt > U561 > ok > U541 > mark1
proper1 > U461 > tt > U561 > ok > U612 > mark1
proper1 > U461 > tt > U561 > ok > U722 > mark1
proper1 > U461 > tt > U561 > ok > U822 > mark1
proper1 > U461 > tt > U561 > ok > isNePal1 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U311 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U321 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U451 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U521 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U541 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U612 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U722 > mark1
proper1 > U461 > tt > U732 > U741 > ok > U822 > mark1
proper1 > U461 > tt > U732 > U741 > ok > isNePal1 > mark1
proper1 > U461 > tt > isPal1 > ok > U311 > mark1
proper1 > U461 > tt > isPal1 > ok > U321 > mark1
proper1 > U461 > tt > isPal1 > ok > U451 > mark1
proper1 > U461 > tt > isPal1 > ok > U521 > mark1
proper1 > U461 > tt > isPal1 > ok > U541 > mark1
proper1 > U461 > tt > isPal1 > ok > U612 > mark1
proper1 > U461 > tt > isPal1 > ok > U722 > mark1
proper1 > U461 > tt > isPal1 > ok > U822 > mark1
proper1 > U461 > tt > isPal1 > ok > isNePal1 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U311 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U321 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U451 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U521 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U541 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U612 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U722 > mark1
proper1 > U551 > isList > tt > isNeList > ok > U822 > mark1
proper1 > U551 > isList > tt > isNeList > ok > isNePal1 > mark1
proper1 > U551 > isList > tt > U441 > ok > U311 > mark1
proper1 > U551 > isList > tt > U441 > ok > U321 > mark1
proper1 > U551 > isList > tt > U441 > ok > U451 > mark1
proper1 > U551 > isList > tt > U441 > ok > U521 > mark1
proper1 > U551 > isList > tt > U441 > ok > U541 > mark1
proper1 > U551 > isList > tt > U441 > ok > U612 > mark1
proper1 > U551 > isList > tt > U441 > ok > U722 > mark1
proper1 > U551 > isList > tt > U441 > ok > U822 > mark1
proper1 > U551 > isList > tt > U441 > ok > isNePal1 > mark1
proper1 > U551 > isList > tt > U561 > ok > U311 > mark1
proper1 > U551 > isList > tt > U561 > ok > U321 > mark1
proper1 > U551 > isList > tt > U561 > ok > U451 > mark1
proper1 > U551 > isList > tt > U561 > ok > U521 > mark1
proper1 > U551 > isList > tt > U561 > ok > U541 > mark1
proper1 > U551 > isList > tt > U561 > ok > U612 > mark1
proper1 > U551 > isList > tt > U561 > ok > U722 > mark1
proper1 > U551 > isList > tt > U561 > ok > U822 > mark1
proper1 > U551 > isList > tt > U561 > ok > isNePal1 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U311 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U321 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U451 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U521 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U541 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U612 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U722 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > U822 > mark1
proper1 > U551 > isList > tt > U732 > U741 > ok > isNePal1 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U311 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U321 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U451 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U521 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U541 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U612 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U722 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > U822 > mark1
proper1 > U551 > isList > tt > isPal1 > ok > isNePal1 > mark1
proper1 > U551 > isList > U211 > ok > U311 > mark1
proper1 > U551 > isList > U211 > ok > U321 > mark1
proper1 > U551 > isList > U211 > ok > U451 > mark1
proper1 > U551 > isList > U211 > ok > U521 > mark1
proper1 > U551 > isList > U211 > ok > U541 > mark1
proper1 > U551 > isList > U211 > ok > U612 > mark1
proper1 > U551 > isList > U211 > ok > U722 > mark1
proper1 > U551 > isList > U211 > ok > U822 > mark1
proper1 > U551 > isList > U211 > ok > isNePal1 > mark1
proper1 > U812 > ok > U311 > mark1
proper1 > U812 > ok > U321 > mark1
proper1 > U812 > ok > U451 > mark1
proper1 > U812 > ok > U521 > mark1
proper1 > U812 > ok > U541 > mark1
proper1 > U812 > ok > U612 > mark1
proper1 > U812 > ok > U722 > mark1
proper1 > U812 > ok > U822 > mark1
proper1 > U812 > ok > isNePal1 > mark1
proper1 > a > mark1
proper1 > e > tt > isNeList > ok > U311 > mark1
proper1 > e > tt > isNeList > ok > U321 > mark1
proper1 > e > tt > isNeList > ok > U451 > mark1
proper1 > e > tt > isNeList > ok > U521 > mark1
proper1 > e > tt > isNeList > ok > U541 > mark1
proper1 > e > tt > isNeList > ok > U612 > mark1
proper1 > e > tt > isNeList > ok > U722 > mark1
proper1 > e > tt > isNeList > ok > U822 > mark1
proper1 > e > tt > isNeList > ok > isNePal1 > mark1
proper1 > e > tt > U441 > ok > U311 > mark1
proper1 > e > tt > U441 > ok > U321 > mark1
proper1 > e > tt > U441 > ok > U451 > mark1
proper1 > e > tt > U441 > ok > U521 > mark1
proper1 > e > tt > U441 > ok > U541 > mark1
proper1 > e > tt > U441 > ok > U612 > mark1
proper1 > e > tt > U441 > ok > U722 > mark1
proper1 > e > tt > U441 > ok > U822 > mark1
proper1 > e > tt > U441 > ok > isNePal1 > mark1
proper1 > e > tt > U561 > ok > U311 > mark1
proper1 > e > tt > U561 > ok > U321 > mark1
proper1 > e > tt > U561 > ok > U451 > mark1
proper1 > e > tt > U561 > ok > U521 > mark1
proper1 > e > tt > U561 > ok > U541 > mark1
proper1 > e > tt > U561 > ok > U612 > mark1
proper1 > e > tt > U561 > ok > U722 > mark1
proper1 > e > tt > U561 > ok > U822 > mark1
proper1 > e > tt > U561 > ok > isNePal1 > mark1
proper1 > e > tt > U732 > U741 > ok > U311 > mark1
proper1 > e > tt > U732 > U741 > ok > U321 > mark1
proper1 > e > tt > U732 > U741 > ok > U451 > mark1
proper1 > e > tt > U732 > U741 > ok > U521 > mark1
proper1 > e > tt > U732 > U741 > ok > U541 > mark1
proper1 > e > tt > U732 > U741 > ok > U612 > mark1
proper1 > e > tt > U732 > U741 > ok > U722 > mark1
proper1 > e > tt > U732 > U741 > ok > U822 > mark1
proper1 > e > tt > U732 > U741 > ok > isNePal1 > mark1
proper1 > e > tt > isPal1 > ok > U311 > mark1
proper1 > e > tt > isPal1 > ok > U321 > mark1
proper1 > e > tt > isPal1 > ok > U451 > mark1
proper1 > e > tt > isPal1 > ok > U521 > mark1
proper1 > e > tt > isPal1 > ok > U541 > mark1
proper1 > e > tt > isPal1 > ok > U612 > mark1
proper1 > e > tt > isPal1 > ok > U722 > mark1
proper1 > e > tt > isPal1 > ok > U822 > mark1
proper1 > e > tt > isPal1 > ok > isNePal1 > mark1
proper1 > i > mark1
proper1 > o > mark1
proper1 > u > ok > U311 > mark1
proper1 > u > ok > U321 > mark1
proper1 > u > ok > U451 > mark1
proper1 > u > ok > U521 > mark1
proper1 > u > ok > U541 > mark1
proper1 > u > ok > U612 > mark1
proper1 > u > ok > U722 > mark1
proper1 > u > ok > U822 > mark1
proper1 > u > ok > isNePal1 > mark1
top > mark1

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

(319) Obligation:

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

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

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

(320) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


ACTIVE(U63(X)) → ACTIVE(X)
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
ACTIVE(x1)  =  ACTIVE(x1)
U63(x1)  =  U63(x1)
active(x1)  =  active(x1)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  mark(x1)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  isPalListKind
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)  =  x1
U26(x1)  =  U26(x1)
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  U33(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)  =  U46(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)  =  x1
U62(x1, x2)  =  U62(x1)
U71(x1, x2, x3)  =  x1
U72(x1, x2)  =  U72(x1)
U73(x1, x2)  =  U73(x1)
isPal(x1)  =  isPal
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1)
U82(x1, x2)  =  x1
U83(x1)  =  U83(x1)
isNePal(x1)  =  isNePal
U91(x1, x2)  =  U91(x1)
U92(x1)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
proper(x1)  =  x1
ok(x1)  =  x1
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
ACTIVE1 > top
active1 > _2 > U513 > mark1 > top
active1 > _2 > U911 > mark1 > top
active1 > U112 > U122 > U131 > tt > U433 > mark1 > top
active1 > U112 > U122 > U131 > tt > U523 > mark1 > top
active1 > U112 > U122 > U131 > tt > isPal > top
active1 > U112 > U122 > U131 > tt > isNePal > mark1 > top
active1 > U213 > U223 > U233 > mark1 > top
active1 > U243 > mark1 > top
active1 > U252 > mark1 > top
active1 > U261 > tt > U433 > mark1 > top
active1 > U261 > tt > U523 > mark1 > top
active1 > U261 > tt > isPal > top
active1 > U261 > tt > isNePal > mark1 > top
active1 > U322 > U331 > tt > U433 > mark1 > top
active1 > U322 > U331 > tt > U523 > mark1 > top
active1 > U322 > U331 > tt > isPal > top
active1 > U322 > U331 > tt > isNePal > mark1 > top
active1 > isQid > tt > U433 > mark1 > top
active1 > isQid > tt > U523 > mark1 > top
active1 > isQid > tt > isPal > top
active1 > isQid > tt > isNePal > mark1 > top
active1 > U413 > U423 > U433 > mark1 > top
active1 > U443 > mark1 > top
active1 > U452 > mark1 > top
active1 > U461 > tt > U433 > mark1 > top
active1 > U461 > tt > U523 > mark1 > top
active1 > U461 > tt > isPal > top
active1 > U461 > tt > isNePal > mark1 > top
active1 > U533 > isPalListKind > tt > U433 > mark1 > top
active1 > U533 > isPalListKind > tt > U523 > mark1 > top
active1 > U533 > isPalListKind > tt > isPal > top
active1 > U533 > isPalListKind > tt > isNePal > mark1 > top
active1 > U533 > isPalListKind > U911 > mark1 > top
active1 > U533 > U543 > isNeList1 > U312 > mark1 > top
active1 > U533 > U543 > isNeList1 > U513 > mark1 > top
active1 > U533 > U543 > U552 > mark1 > top
active1 > U621 > U631 > mark1 > top
active1 > U721 > mark1 > top
active1 > U721 > isPal > top
active1 > U731 > mark1 > top
active1 > U811 > mark1 > top
active1 > U831 > tt > U433 > mark1 > top
active1 > U831 > tt > U523 > mark1 > top
active1 > U831 > tt > isPal > top
active1 > U831 > tt > isNePal > mark1 > top
active1 > U921 > tt > U433 > mark1 > top
active1 > U921 > tt > U523 > mark1 > top
active1 > U921 > tt > isPal > top
active1 > U921 > tt > isNePal > mark1 > top
nil > mark1 > top
a > mark1 > top
e > tt > U433 > mark1 > top
e > tt > U523 > mark1 > top
e > tt > isPal > top
e > tt > isNePal > mark1 > top
i > tt > U433 > mark1 > top
i > tt > U523 > mark1 > top
i > tt > isPal > top
i > tt > isNePal > mark1 > top
o > mark1 > top
u > top

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

(321) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(322) PisEmptyProof (EQUIVALENT transformation)

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

(323) TRUE

(324) Obligation:

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

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

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

(325) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


TOP(mark(X)) → TOP(proper(X))
The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
TOP(x1)  =  x1
ok(x1)  =  x1
active(x1)  =  x1
mark(x1)  =  mark(x1)
proper(x1)  =  x1
__(x1, x2)  =  __(x1, x2)
nil  =  nil
U11(x1, x2)  =  U11(x1, x2)
tt  =  tt
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
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, x2)
U33(x1)  =  U33(x1)
isQid(x1)  =  x1
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  U46(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)  =  U56(x1)
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  U63(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)  =  U74(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)  =  U92(x1)
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
top(x1)  =  top

Lexicographic Path Order [LPO].
Precedence:
_2 > U213 > U223 > U233 > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
_2 > U213 > U223 > U233 > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U213 > U223 > U233 > U243 > U252 > U261 > mark1
_2 > U413 > U423 > U433 > U443 > isList1 > U112 > U122 > U131 > mark1
_2 > U413 > U423 > U433 > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U413 > U423 > U433 > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U413 > U423 > U433 > U443 > U452 > U461 > mark1
_2 > U513 > U523 > U533 > U543 > U552 > isList1 > U112 > U122 > U131 > mark1
_2 > U513 > U523 > U533 > U543 > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U513 > U523 > U533 > U543 > U552 > U561 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U243 > U252 > U261 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U443 > isList1 > U112 > U122 > U131 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U443 > U452 > U461 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U552 > isList1 > U112 > U122 > U131 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U552 > U561 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U622 > U631 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U831 > mark1
_2 > U713 > U722 > U732 > U741 > tt > U921 > mark1
_2 > U713 > U722 > isPal1 > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
_2 > U713 > U722 > isPal1 > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > isPal1 > tt > U243 > U252 > U261 > mark1
_2 > U713 > U722 > isPal1 > tt > U443 > isList1 > U112 > U122 > U131 > mark1
_2 > U713 > U722 > isPal1 > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > isPal1 > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > isPal1 > tt > U443 > U452 > U461 > mark1
_2 > U713 > U722 > isPal1 > tt > U552 > isList1 > U112 > U122 > U131 > mark1
_2 > U713 > U722 > isPal1 > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
_2 > U713 > U722 > isPal1 > tt > U552 > U561 > mark1
_2 > U713 > U722 > isPal1 > tt > U622 > U631 > mark1
_2 > U713 > U722 > isPal1 > tt > U831 > mark1
_2 > U713 > U722 > isPal1 > tt > U921 > mark1
_2 > U713 > U722 > isPal1 > U812 > U822 > U831 > mark1
_2 > U713 > U722 > isPal1 > U812 > U822 > isNePal1 > U612 > U622 > U631 > mark1
_2 > U912 > U921 > mark1
nil > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
nil > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
nil > tt > U243 > U252 > U261 > mark1
nil > tt > U443 > isList1 > U112 > U122 > U131 > mark1
nil > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
nil > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
nil > tt > U443 > U452 > U461 > mark1
nil > tt > U552 > isList1 > U112 > U122 > U131 > mark1
nil > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
nil > tt > U552 > U561 > mark1
nil > tt > U622 > U631 > mark1
nil > tt > U831 > mark1
nil > tt > U921 > mark1
a > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
a > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
a > tt > U243 > U252 > U261 > mark1
a > tt > U443 > isList1 > U112 > U122 > U131 > mark1
a > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
a > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
a > tt > U443 > U452 > U461 > mark1
a > tt > U552 > isList1 > U112 > U122 > U131 > mark1
a > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
a > tt > U552 > U561 > mark1
a > tt > U622 > U631 > mark1
a > tt > U831 > mark1
a > tt > U921 > mark1
e > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
e > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
e > tt > U243 > U252 > U261 > mark1
e > tt > U443 > isList1 > U112 > U122 > U131 > mark1
e > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
e > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
e > tt > U443 > U452 > U461 > mark1
e > tt > U552 > isList1 > U112 > U122 > U131 > mark1
e > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
e > tt > U552 > U561 > mark1
e > tt > U622 > U631 > mark1
e > tt > U831 > mark1
e > tt > U921 > mark1
i > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
i > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
i > tt > U243 > U252 > U261 > mark1
i > tt > U443 > isList1 > U112 > U122 > U131 > mark1
i > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
i > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
i > tt > U443 > U452 > U461 > mark1
i > tt > U552 > isList1 > U112 > U122 > U131 > mark1
i > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
i > tt > U552 > U561 > mark1
i > tt > U622 > U631 > mark1
i > tt > U831 > mark1
i > tt > U921 > mark1
o > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
o > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
o > tt > U243 > U252 > U261 > mark1
o > tt > U443 > isList1 > U112 > U122 > U131 > mark1
o > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
o > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
o > tt > U443 > U452 > U461 > mark1
o > tt > U552 > isList1 > U112 > U122 > U131 > mark1
o > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
o > tt > U552 > U561 > mark1
o > tt > U622 > U631 > mark1
o > tt > U831 > mark1
o > tt > U921 > mark1
u > tt > U243 > U252 > isList1 > U112 > U122 > U131 > mark1
u > tt > U243 > U252 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
u > tt > U243 > U252 > U261 > mark1
u > tt > U443 > isList1 > U112 > U122 > U131 > mark1
u > tt > U443 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
u > tt > U443 > U452 > isNeList1 > U312 > U322 > U331 > mark1
u > tt > U443 > U452 > U461 > mark1
u > tt > U552 > isList1 > U112 > U122 > U131 > mark1
u > tt > U552 > isList1 > U112 > U122 > isNeList1 > U312 > U322 > U331 > mark1
u > tt > U552 > U561 > mark1
u > tt > U622 > U631 > mark1
u > tt > U831 > mark1
u > tt > U921 > mark1
top > mark1

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

(326) Obligation:

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

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

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

(327) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].


The following pairs can be oriented strictly and are deleted.


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

Lexicographic Path Order [LPO].
Precedence:
TOP1 > mark
proper1 > nil > mark
proper1 > U232 > ok1 > mark
proper1 > U243 > isList1 > U111 > ok1 > mark
proper1 > U243 > isList1 > tt > mark
proper1 > U251 > isList1 > U111 > ok1 > mark
proper1 > U251 > isList1 > tt > mark
proper1 > isQid1 > ok1 > mark
proper1 > isQid1 > tt > mark
proper1 > U422 > U433 > ok1 > mark
proper1 > U451 > isNeList1 > ok1 > mark
proper1 > U513 > ok1 > mark
proper1 > U531 > isPalListKind1 > ok1 > mark
proper1 > U531 > isPalListKind1 > tt > mark
proper1 > U551 > isList1 > U111 > ok1 > mark
proper1 > U551 > isList1 > tt > mark
proper1 > U551 > U561 > ok1 > mark
proper1 > U551 > U561 > tt > mark
proper1 > U631 > ok1 > mark
proper1 > U631 > tt > mark
proper1 > U731 > U741 > ok1 > mark
proper1 > U731 > U741 > tt > mark
proper1 > U812 > U822 > ok1 > mark
proper1 > U831 > ok1 > mark
proper1 > U831 > tt > mark
proper1 > isNePal1 > U612 > ok1 > mark
proper1 > isNePal1 > U712 > U721 > ok1 > mark
proper1 > a > mark
proper1 > e > ok1 > mark
proper1 > e > tt > mark
proper1 > i > ok1 > mark
proper1 > i > tt > mark
proper1 > o > mark
proper1 > u > mark
top > mark

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

(328) 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)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X1), X2) → mark(U12(X1, X2))
U13(mark(X)) → mark(U13(X))
U21(mark(X1), X2, X3) → mark(U21(X1, X2, X3))
U22(mark(X1), X2, X3) → mark(U22(X1, X2, X3))
U23(mark(X1), X2, X3) → mark(U23(X1, X2, X3))
U24(mark(X1), X2, X3) → mark(U24(X1, X2, X3))
U25(mark(X1), X2) → mark(U25(X1, X2))
U26(mark(X)) → mark(U26(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X1), X2) → mark(U32(X1, X2))
U33(mark(X)) → mark(U33(X))
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3))
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3))
U43(mark(X1), X2, X3) → mark(U43(X1, X2, X3))
U44(mark(X1), X2, X3) → mark(U44(X1, X2, X3))
U45(mark(X1), X2) → mark(U45(X1, X2))
U46(mark(X)) → mark(U46(X))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
U53(mark(X1), X2, X3) → mark(U53(X1, X2, X3))
U54(mark(X1), X2, X3) → mark(U54(X1, X2, X3))
U55(mark(X1), X2) → mark(U55(X1, X2))
U56(mark(X)) → mark(U56(X))
U61(mark(X1), X2) → mark(U61(X1, X2))
U62(mark(X1), X2) → mark(U62(X1, X2))
U63(mark(X)) → mark(U63(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2) → mark(U72(X1, X2))
U73(mark(X1), X2) → mark(U73(X1, X2))
U74(mark(X)) → mark(U74(X))
U81(mark(X1), X2) → mark(U81(X1, X2))
U82(mark(X1), X2) → mark(U82(X1, X2))
U83(mark(X)) → mark(U83(X))
U91(mark(X1), X2) → mark(U91(X1, X2))
U92(mark(X)) → mark(U92(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
__(ok(X1), ok(X2)) → ok(__(X1, X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X1), ok(X2)) → ok(U12(X1, X2))
isPalListKind(ok(X)) → ok(isPalListKind(X))
U13(ok(X)) → ok(U13(X))
isNeList(ok(X)) → ok(isNeList(X))
U21(ok(X1), ok(X2), ok(X3)) → ok(U21(X1, X2, X3))
U22(ok(X1), ok(X2), ok(X3)) → ok(U22(X1, X2, X3))
U23(ok(X1), ok(X2), ok(X3)) → ok(U23(X1, X2, X3))
U24(ok(X1), ok(X2), ok(X3)) → ok(U24(X1, X2, X3))
U25(ok(X1), ok(X2)) → ok(U25(X1, X2))
isList(ok(X)) → ok(isList(X))
U26(ok(X)) → ok(U26(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X1), ok(X2)) → ok(U32(X1, X2))
U33(ok(X)) → ok(U33(X))
isQid(ok(X)) → ok(isQid(X))
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3))
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3))
U43(ok(X1), ok(X2), ok(X3)) → ok(U43(X1, X2, X3))
U44(ok(X1), ok(X2), ok(X3)) → ok(U44(X1, X2, X3))
U45(ok(X1), ok(X2)) → ok(U45(X1, X2))
U46(ok(X)) → ok(U46(X))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
U53(ok(X1), ok(X2), ok(X3)) → ok(U53(X1, X2, X3))
U54(ok(X1), ok(X2), ok(X3)) → ok(U54(X1, X2, X3))
U55(ok(X1), ok(X2)) → ok(U55(X1, X2))
U56(ok(X)) → ok(U56(X))
U61(ok(X1), ok(X2)) → ok(U61(X1, X2))
U62(ok(X1), ok(X2)) → ok(U62(X1, X2))
U63(ok(X)) → ok(U63(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2)) → ok(U72(X1, X2))
U73(ok(X1), ok(X2)) → ok(U73(X1, X2))
isPal(ok(X)) → ok(isPal(X))
U74(ok(X)) → ok(U74(X))
U81(ok(X1), ok(X2)) → ok(U81(X1, X2))
U82(ok(X1), ok(X2)) → ok(U82(X1, X2))
U83(ok(X)) → ok(U83(X))
isNePal(ok(X)) → ok(isNePal(X))
U91(ok(X1), ok(X2)) → ok(U91(X1, X2))
U92(ok(X)) → ok(U92(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

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

(329) PisEmptyProof (EQUIVALENT transformation)

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

(330) TRUE