Termination w.r.t. Q proof of /tmp/tmppltlWr/PALINDROME_complete_noand

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

0 QTRS

↳1 DependencyPairsProof (⇔)

↳2 QDP

↳3 DependencyGraphProof (⇔)

↳4 AND

  ↳5 QDP

    ↳6 QDPOrderProof (⇔)

    ↳7 QDP

    ↳8 PisEmptyProof (⇔)

    ↳9 TRUE

  ↳10 QDP

    ↳11 QDPOrderProof (⇔)

    ↳12 QDP

    ↳13 DependencyGraphProof (⇔)

    ↳14 TRUE

  ↳15 QDP

    ↳16 QDPOrderProof (⇔)

    ↳17 QDP

    ↳18 DependencyGraphProof (⇔)

    ↳19 TRUE

  ↳20 QDP

    ↳21 QDPOrderProof (⇔)

    ↳22 QDP

    ↳23 DependencyGraphProof (⇔)

    ↳24 QDP

    ↳25 QDPOrderProof (⇔)

    ↳26 QDP

    ↳27 QDPOrderProof (⇔)

    ↳28 QDP

    ↳29 QDPOrderProof (⇔)

    ↳30 QDP

    ↳31 QDPOrderProof (⇔)

    ↳32 QDP

    ↳33 QDPOrderProof (⇔)

    ↳34 QDP

    ↳35 QDPOrderProof (⇔)

    ↳36 QDP

    ↳37 QDPOrderProof (⇔)

    ↳38 QDP

    ↳39 QDPOrderProof (⇔)

    ↳40 QDP

    ↳41 QDPOrderProof (⇔)

    ↳42 QDP

    ↳43 QDPOrderProof (⇔)

    ↳44 QDP

    ↳45 QDPOrderProof (⇔)

    ↳46 QDP

    ↳47 QDPOrderProof (⇔)

    ↳48 QDP

    ↳49 QDPOrderProof (⇔)

    ↳50 QDP

    ↳51 QDPOrderProof (⇔)

    ↳52 QDP

    ↳53 QDPOrderProof (⇔)

    ↳54 QDP

    ↳55 PisEmptyProof (⇔)

    ↳56 TRUE

(0) Obligation:

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

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.

(1) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(2) Obligation:

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

A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
A____(__(X, Y), Z) → MARK(X)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__U11(tt, V) → A__ISPALLISTKIND(V)
A__U12(tt, V) → A__U13(a__isNeList(V))
A__U12(tt, V) → A__ISNELIST(V)
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
A__U21(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
A__U22(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)
A__U23(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
A__U24(tt, V1, V2) → A__ISLIST(V1)
A__U25(tt, V2) → A__U26(a__isList(V2))
A__U25(tt, V2) → A__ISLIST(V2)
A__U31(tt, V) → A__U32(a__isPalListKind(V), V)
A__U31(tt, V) → A__ISPALLISTKIND(V)
A__U32(tt, V) → A__U33(a__isQid(V))
A__U32(tt, V) → A__ISQID(V)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
A__U41(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
A__U42(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
A__U43(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
A__U44(tt, V1, V2) → A__ISLIST(V1)
A__U45(tt, V2) → A__U46(a__isNeList(V2))
A__U45(tt, V2) → A__ISNELIST(V2)
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__U51(tt, V1, V2) → A__ISPALLISTKIND(V1)
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
A__U52(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
A__U53(tt, V1, V2) → A__ISPALLISTKIND(V2)
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U55(tt, V2) → A__U56(a__isList(V2))
A__U55(tt, V2) → A__ISLIST(V2)
A__U61(tt, V) → A__U62(a__isPalListKind(V), V)
A__U61(tt, V) → A__ISPALLISTKIND(V)
A__U62(tt, V) → A__U63(a__isQid(V))
A__U62(tt, V) → A__ISQID(V)
A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
A__U71(tt, I, P) → A__ISPALLISTKIND(I)
A__U72(tt, P) → A__U73(a__isPal(P), P)
A__U72(tt, P) → A__ISPAL(P)
A__U73(tt, P) → A__U74(a__isPalListKind(P))
A__U73(tt, P) → A__ISPALLISTKIND(P)
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)
A__U81(tt, V) → A__ISPALLISTKIND(V)
A__U82(tt, V) → A__U83(a__isNePal(V))
A__U82(tt, V) → A__ISNEPAL(V)
A__U91(tt, V2) → A__U92(a__isPalListKind(V2))
A__U91(tt, V2) → A__ISPALLISTKIND(V2)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__ISLIST(V) → A__ISPALLISTKIND(V)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
A__ISLIST(__(V1, V2)) → A__ISPALLISTKIND(V1)
A__ISNELIST(V) → A__U31(a__isPalListKind(V), V)
A__ISNELIST(V) → A__ISPALLISTKIND(V)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__ISNELIST(__(V1, V2)) → A__ISPALLISTKIND(V1)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__ISNEPAL(V) → A__U61(a__isPalListKind(V), V)
A__ISNEPAL(V) → A__ISPALLISTKIND(V)
A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
A__ISNEPAL(__(I, __(P, I))) → A__ISQID(I)
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
A__ISPAL(V) → A__ISPALLISTKIND(V)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U11(X1, X2)) → A__U11(mark(X1), X2)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U12(X1, X2)) → A__U12(mark(X1), X2)
MARK(U12(X1, X2)) → MARK(X1)
MARK(isPalListKind(X)) → A__ISPALLISTKIND(X)
MARK(U13(X)) → A__U13(mark(X))
MARK(U13(X)) → MARK(X)
MARK(isNeList(X)) → A__ISNELIST(X)
MARK(U21(X1, X2, X3)) → A__U21(mark(X1), X2, X3)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → A__U22(mark(X1), X2, X3)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → A__U23(mark(X1), X2, X3)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → A__U24(mark(X1), X2, X3)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → A__U25(mark(X1), X2)
MARK(U25(X1, X2)) → MARK(X1)
MARK(isList(X)) → A__ISLIST(X)
MARK(U26(X)) → A__U26(mark(X))
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → A__U31(mark(X1), X2)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → A__U32(mark(X1), X2)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → A__U33(mark(X))
MARK(U33(X)) → MARK(X)
MARK(isQid(X)) → A__ISQID(X)
MARK(U41(X1, X2, X3)) → A__U41(mark(X1), X2, X3)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → A__U42(mark(X1), X2, X3)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → A__U43(mark(X1), X2, X3)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → A__U44(mark(X1), X2, X3)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → A__U45(mark(X1), X2)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → A__U46(mark(X))
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → A__U51(mark(X1), X2, X3)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → A__U52(mark(X1), X2, X3)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → A__U53(mark(X1), X2, X3)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → A__U54(mark(X1), X2, X3)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → A__U55(mark(X1), X2)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → A__U56(mark(X))
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → A__U61(mark(X1), X2)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → A__U62(mark(X1), X2)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → A__U63(mark(X))
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → A__U71(mark(X1), X2, X3)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → A__U72(mark(X1), X2)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → A__U73(mark(X1), X2)
MARK(U73(X1, X2)) → MARK(X1)
MARK(isPal(X)) → A__ISPAL(X)
MARK(U74(X)) → A__U74(mark(X))
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → A__U81(mark(X1), X2)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → A__U82(mark(X1), X2)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → A__U83(mark(X))
MARK(U83(X)) → MARK(X)
MARK(isNePal(X)) → A__ISNEPAL(X)
MARK(U91(X1, X2)) → A__U91(mark(X1), X2)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → A__U92(mark(X))
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(3) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 4 SCCs with 80 less nodes.

(4) Complex Obligation (AND)

(5) Obligation:

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

A__U91(tt, V2) → A__ISPALLISTKIND(V2)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(6) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

A__U91(tt, V2) → A__ISPALLISTKIND(V2)
A__ISPALLISTKIND(__(V1, V2)) → A__U91(a__isPalListKind(V1), V2)
A__ISPALLISTKIND(__(V1, V2)) → A__ISPALLISTKIND(V1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A__U91(x1, x2) = A__U91(x1, x2)
tt = tt
A__ISPALLISTKIND(x1) = A__ISPALLISTKIND(x1)
__(x1, x2) = __(x1, x2)
a__isPalListKind(x1) = x1
a__U91(x1, x2) = x2
u = u
o = o
nil = nil
i = i
a__U92(x1) = x1
e = e
U91(x1, x2) = x2
a = a
U92(x1) = x1
isPalListKind(x1) = x1

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

__₂ > A_{_U91₂} > A_{_{ISPALLISTKIND₁}}
u > tt
o > tt
nil > tt
i > tt
e > tt
a > tt

Status:

i: []
a: []
tt: []
__₂: [1,2]
A_{_U91₂}: [2,1]
u: []
e: []
o: []
A_{_{ISPALLISTKIND₁}}: [1]
nil: []

The following usable rules [FROCOS05] were oriented:

a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt
a__isPalListKind(o) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(i) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__isPalListKind(e) → tt
a__U92(tt) → tt
a__U91(X1, X2) → U91(X1, X2)
a__isPalListKind(a) → tt
a__U92(X) → U92(X)
a__isPalListKind(X) → isPalListKind(X)

(7) Obligation:

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

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(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:

A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
A__U72(tt, P) → A__ISPAL(P)
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)
A__U82(tt, V) → A__ISNEPAL(V)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(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.

A__ISNEPAL(__(I, __(P, I))) → A__U71(a__isQid(I), I, P)
A__U72(tt, P) → A__ISPAL(P)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A__ISNEPAL(x1) = A__ISNEPAL(x1)
__(x1, x2) = __(x1, x2)
A__U71(x1, x2, x3) = A__U71(x1, x3)
a__isQid(x1) = a__isQid
tt = tt
A__U72(x1, x2) = A__U72(x1, x2)
a__isPalListKind(x1) = a__isPalListKind
A__ISPAL(x1) = A__ISPAL(x1)
A__U81(x1, x2) = A__U81(x2)
A__U82(x1, x2) = A__U82(x2)
isQid(x1) = isQid
a__U91(x1, x2) = a__U91
a__U92(x1) = x1
U91(x1, x2) = U91
U92(x1) = x1
isPalListKind(x1) = isPalListKind
u = u
o = o
nil = nil
i = i
e = e
a = a

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

[_{_₂}, A_{_U71₂}, a_{_isQid}, tt, A_{_U72₂}, a_{_{isPalListKind}}, a_{_U91}, U91] > [A_{_ISNEPAL₁}, A_{_ISPAL₁}, A_{_U81₁}, A_{_U82₁}]
[_{_₂}, A_{_U71₂}, a_{_isQid}, tt, A_{_U72₂}, a_{_{isPalListKind}}, a_{_U91}, U91] > isQid
[_{_₂}, A_{_U71₂}, a_{_isQid}, tt, A_{_U72₂}, a_{_{isPalListKind}}, a_{_U91}, U91] > isPalListKind

Status:

i: []
A_{_U71₂}: [1,2]
A_{_ISPAL₁}: [1]
a: []
__₂: [2,1]
a_{_isQid}: []
U91: []
e: []
A_{_ISNEPAL₁}: [1]
isPalListKind: []
o: []
A_{_U72₂}: [1,2]
a_{_{isPalListKind}}: []
tt: []
u: []
A_{_U82₁}: [1]
A_{_U81₁}: [1]
a_{_U91}: []
isQid: []
nil: []

The following usable rules [FROCOS05] were oriented:

a__isQid(X) → isQid(X)
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)
a__isPalListKind(X) → isPalListKind(X)
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt
a__isPalListKind(o) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(i) → tt
a__isPalListKind(e) → tt
a__isPalListKind(a) → tt
a__isQid(u) → tt
a__isQid(o) → tt
a__isQid(i) → tt
a__isQid(e) → tt
a__isQid(a) → tt

(12) Obligation:

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

A__U71(tt, I, P) → A__U72(a__isPalListKind(I), P)
A__ISPAL(V) → A__U81(a__isPalListKind(V), V)
A__U81(tt, V) → A__U82(a__isPalListKind(V), V)
A__U82(tt, V) → A__ISNEPAL(V)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(13) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(14) TRUE

(15) Obligation:

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

A__U12(tt, V) → A__ISNELIST(V)
A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
A__U45(tt, V2) → A__ISNELIST(V2)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
A__U55(tt, V2) → A__ISLIST(V2)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
A__U25(tt, V2) → A__ISLIST(V2)
A__U24(tt, V1, V2) → A__ISLIST(V1)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U44(tt, V1, V2) → A__ISLIST(V1)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(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.

A__ISNELIST(__(V1, V2)) → A__U41(a__isPalListKind(V1), V1, V2)
A__U44(tt, V1, V2) → A__U45(a__isList(V1), V2)
A__U51(tt, V1, V2) → A__U52(a__isPalListKind(V1), V1, V2)
A__U52(tt, V1, V2) → A__U53(a__isPalListKind(V2), V1, V2)
A__U54(tt, V1, V2) → A__U55(a__isNeList(V1), V2)
A__U11(tt, V) → A__U12(a__isPalListKind(V), V)
A__ISLIST(__(V1, V2)) → A__U21(a__isPalListKind(V1), V1, V2)
A__U24(tt, V1, V2) → A__U25(a__isList(V1), V2)
A__U25(tt, V2) → A__ISLIST(V2)
A__U24(tt, V1, V2) → A__ISLIST(V1)
A__U54(tt, V1, V2) → A__ISNELIST(V1)
A__U44(tt, V1, V2) → A__ISLIST(V1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A__U12(x1, x2) = x2
tt = tt
A__ISNELIST(x1) = x1
__(x1, x2) = __(x1, x2)
A__U41(x1, x2, x3) = A__U41(x2, x3)
a__isPalListKind(x1) = a__isPalListKind
A__U42(x1, x2, x3) = A__U42(x2, x3)
A__U43(x1, x2, x3) = A__U43(x2, x3)
A__U44(x1, x2, x3) = A__U44(x2, x3)
A__U45(x1, x2) = x2
a__isList(x1) = a__isList
A__U51(x1, x2, x3) = A__U51(x2, x3)
A__U52(x1, x2, x3) = A__U52(x2, x3)
A__U53(x1, x2, x3) = A__U53(x2, x3)
A__U54(x1, x2, x3) = A__U54(x2, x3)
A__U55(x1, x2) = A__U55(x2)
a__isNeList(x1) = a__isNeList
A__ISLIST(x1) = A__ISLIST(x1)
A__U11(x1, x2) = A__U11(x2)
A__U21(x1, x2, x3) = A__U21(x2, x3)
A__U22(x1, x2, x3) = A__U22(x2, x3)
A__U23(x1, x2, x3) = A__U23(x2, x3)
A__U24(x1, x2, x3) = A__U24(x2, x3)
A__U25(x1, x2) = A__U25(x1, x2)
a__U11(x1, x2) = a__U11
a__U12(x1, x2) = a__U12
a__U21(x1, x2, x3) = a__U21
a__U22(x1, x2, x3) = a__U22
a__U23(x1, x2, x3) = a__U23
a__U91(x1, x2) = x1
U91(x1, x2) = x1
a__U13(x1) = a__U13
a__U92(x1) = a__U92
U92(x1) = U92
a__U25(x1, x2) = a__U25
a__U26(x1) = a__U26
a__U24(x1, x2, x3) = a__U24
a__U33(x1) = a__U33
a__U41(x1, x2, x3) = a__U41
a__U42(x1, x2, x3) = a__U42
a__U31(x1, x2) = a__U31(x1, x2)
a__U32(x1, x2) = a__U32
a__isQid(x1) = a__isQid
U31(x1, x2) = U31(x1)
U32(x1, x2) = U32(x1, x2)
U33(x1) = x1
isQid(x1) = isQid
U24(x1, x2, x3) = U24
U25(x1, x2) = U25
isList(x1) = isList
U26(x1) = U26
nil = nil
isNeList(x1) = x1
U21(x1, x2, x3) = U21
U22(x1, x2, x3) = U22
U23(x1, x2, x3) = U23
a__U51(x1, x2, x3) = a__U51
U11(x1, x2) = U11
U12(x1, x2) = U12
isPalListKind(x1) = isPalListKind
U13(x1) = U13
a__U43(x1, x2, x3) = a__U43
a__U44(x1, x2, x3) = a__U44
a__U45(x1, x2) = a__U45
a__U46(x1) = a__U46
a__U54(x1, x2, x3) = a__U54
U54(x1, x2, x3) = U54
a__U52(x1, x2, x3) = a__U52
a__U53(x1, x2, x3) = x1
U53(x1, x2, x3) = U53
a__U56(x1) = a__U56
U56(x1) = U56
a__U55(x1, x2) = a__U55
U55(x1, x2) = U55
U46(x1) = U46
U45(x1, x2) = U45
U52(x1, x2, x3) = U52
U51(x1, x2, x3) = U51
U42(x1, x2, x3) = U42
U41(x1, x2, x3) = U41
U44(x1, x2, x3) = U44
U43(x1, x2, x3) = U43
u = u
o = o
i = i
e = e
a = a

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

[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > a_{_U31₂} > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > isPalListKind > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_{isPalListKind}}, a_{_U51}, a_{_U52}, U52] > U51 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > [a_{_U46}, U46] > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > [a_{_U43}, U43] > [a_{_U44}, a_{_U45}, U44] > U45 > [U53, U55]
[a_{_isNeList}, a_{_U41}, a_{_U42}, U42] > U41 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
a_{_U33} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
[a_{_U32}, U32₂] > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
a_{_isQid} > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
U31₁ > [U53, U55]
isQid > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
nil > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
u > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
o > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
i > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
e > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > [A_{_U41₂}, A_{_U42₂}, A_{_U43₂}, A_{_U44₂}] > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U52₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > A_{_U25₂} > [A_{_U53₂}, A_{_U54₂}, A_{_U55₁}, A_{_ISLIST₁}, A_{_U11₁}] > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U92 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U22 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U23 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U11 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U12 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U13 > [U53, U55]
a > [tt, _{_₂}, a_{_isList}, A_{_U51₂}, A_{_U21₂}, A_{_U22₂}, A_{_U23₂}, A_{_U24₂}, a_{_U11}, a_{_U12}, a_{_U21}, a_{_U22}, a_{_U23}, a_{_U13}, a_{_U92}, a_{_U25}, a_{_U26}, a_{_U24}, U24, U25, isList, U26, U21, a_{_U54}, U54, a_{_U56}, a_{_U55}] > U56 > [U53, U55]

Status:

i: []
a_{_U33}: []
U22: []
a_{_U54}: []
U92: []
a_{_U24}: []
U32₂: [2,1]
U55: []
U42: []
U11: []
a_{_U41}: []
A_{_U23₂}: [1,2]
a_{_U43}: []
tt: []
a_{_U45}: []
A_{_U42₂}: [1,2]
a_{_U92}: []
U41: []
a_{_U32}: []
nil: []
U25: []
U51: []
a_{_U46}: []
A_{_U44₂}: [1,2]
e: []
a_{_isList}: []
A_{_U53₂}: [2,1]
o: []
a_{_U26}: []
a_{_U44}: []
a_{_U31₂}: [2,1]
U31₁: [1]
a_{_U25}: []
U45: []
A_{_U54₂}: [2,1]
A_{_U43₂}: [1,2]
a_{_U21}: []
U56: []
__₂: [1,2]
isPalListKind: []
U44: []
A_{_U24₂}: [1,2]
a_{_U13}: []
A_{_U41₂}: [1,2]
U54: []
a_{_U52}: []
a_{_{isPalListKind}}: []
isList: []
U24: []
A_{_U52₂}: [1,2]
a_{_U12}: []
isQid: []
U23: []
U43: []
a_{_U56}: []
U13: []
U26: []
U21: []
U46: []
a: []
A_{_U22₂}: [1,2]
a_{_isQid}: []
a_{_U42}: []
a_{_U11}: []
U53: []
a_{_U55}: []
U52: []
U12: []
A_{_U55₁}: [1]
a_{_U22}: []
A_{_U11₁}: [1]
A_{_U21₂}: [1,2]
A_{_U51₂}: [1,2]
a_{_isNeList}: []
u: []
A_{_U25₂}: [1,2]
a_{_U51}: []
A_{_ISLIST₁}: [1]
a_{_U23}: []

The following usable rules [FROCOS05] were oriented:

a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U91(X1, X2) → U91(X1, X2)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U92(X) → U92(X)
a__U13(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U25(X1, X2) → U25(X1, X2)
a__U92(tt) → tt
a__isList(X) → isList(X)
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__U26(X) → U26(X)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U46(tt) → tt
a__U56(X) → U56(X)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U55(X1, X2) → U55(X1, X2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U46(X) → U46(X)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U45(X1, X2) → U45(X1, X2)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U56(tt) → tt
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt
a__isPalListKind(o) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(i) → tt
a__isPalListKind(e) → tt
a__isPalListKind(a) → tt

(17) Obligation:

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

A__U12(tt, V) → A__ISNELIST(V)
A__U41(tt, V1, V2) → A__U42(a__isPalListKind(V1), V1, V2)
A__U42(tt, V1, V2) → A__U43(a__isPalListKind(V2), V1, V2)
A__U43(tt, V1, V2) → A__U44(a__isPalListKind(V2), V1, V2)
A__U45(tt, V2) → A__ISNELIST(V2)
A__ISNELIST(__(V1, V2)) → A__U51(a__isPalListKind(V1), V1, V2)
A__U53(tt, V1, V2) → A__U54(a__isPalListKind(V2), V1, V2)
A__U55(tt, V2) → A__ISLIST(V2)
A__ISLIST(V) → A__U11(a__isPalListKind(V), V)
A__U21(tt, V1, V2) → A__U22(a__isPalListKind(V1), V1, V2)
A__U22(tt, V1, V2) → A__U23(a__isPalListKind(V2), V1, V2)
A__U23(tt, V1, V2) → A__U24(a__isPalListKind(V2), V1, V2)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(18) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 12 less nodes.

(19) TRUE

(20) Obligation:

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

A____(__(X, Y), Z) → MARK(X)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U12(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(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.

A____(__(X, Y), Z) → MARK(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
A____(x1, x2) = A____(x1, x2)
__(x1, x2) = __(x1, x2)
MARK(x1) = x1
mark(x1) = x1
a____(x1, x2) = a____(x1, x2)
U11(x1, x2) = x1
U12(x1, x2) = x1
U13(x1) = x1
U21(x1, x2, x3) = x1
U22(x1, x2, x3) = x1
U23(x1, x2, x3) = x1
U24(x1, x2, x3) = x1
U25(x1, x2) = x1
U26(x1) = x1
U31(x1, x2) = x1
U32(x1, x2) = x1
U33(x1) = x1
U41(x1, x2, x3) = x1
U42(x1, x2, x3) = x1
U43(x1, x2, x3) = x1
U44(x1, x2, x3) = x1
U45(x1, x2) = x1
U46(x1) = x1
U51(x1, x2, x3) = x1
U52(x1, x2, x3) = x1
U53(x1, x2, x3) = 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) = x1
U72(x1, x2) = x1
U73(x1, x2) = x1
U74(x1) = x1
U81(x1, x2) = x1
U82(x1, x2) = x1
U83(x1) = x1
U91(x1, x2) = x1
U92(x1) = x1
nil = nil
a__U11(x1, x2) = x1
tt = tt
a__U12(x1, x2) = x1
a__isPalListKind(x1) = a__isPalListKind
a__U21(x1, x2, x3) = x1
a__U22(x1, x2, x3) = x1
a__U23(x1, x2, x3) = x1
a__U13(x1) = x1
a__isNeList(x1) = a__isNeList
a__U25(x1, x2) = x1
a__U26(x1) = x1
a__isList(x1) = a__isList
a__U24(x1, x2, x3) = x1
a__U33(x1) = x1
a__U41(x1, x2, x3) = x1
a__U42(x1, x2, x3) = x1
a__U31(x1, x2) = x1
a__U32(x1, x2) = x1
a__isQid(x1) = a__isQid
a__U73(x1, x2) = x1
a__U74(x1) = x1
a__U81(x1, x2) = x1
a__U82(x1, x2) = x1
a__U83(x1) = x1
a__isNePal(x1) = a__isNePal
a__U91(x1, x2) = x1
a__U92(x1) = x1
a__U51(x1, x2, x3) = x1
a__U61(x1, x2) = x1
a__U71(x1, x2, x3) = x1
a__isPal(x1) = a__isPal
a__U43(x1, x2, x3) = x1
a__U44(x1, x2, x3) = x1
a__U45(x1, x2) = x1
a__U46(x1) = x1
a__U52(x1, x2, x3) = x1
a__U53(x1, x2, x3) = x1
a__U54(x1, x2, x3) = x1
a__U55(x1, x2) = x1
a__U56(x1) = x1
a__U62(x1, x2) = x1
a__U63(x1) = x1
a__U72(x1, x2) = x1
isNeList(x1) = isNeList
isPalListKind(x1) = isPalListKind
isQid(x1) = isQid
isList(x1) = isList
u = u
o = o
i = i
e = e
a = a
isNePal(x1) = isNePal
isPal(x1) = isPal

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

[A_{_{_{_₂}}}, _{_₂}, a_{_{_{_₂}}}]
i > [tt, a_{_{isPalListKind}}, a_{_isNeList}, a_{_isList}, a_{_isQid}, a_{_isNePal}, a_{_isPal}, isNeList, isPalListKind, isQid, isList, isNePal, isPal]
e > [tt, a_{_{isPalListKind}}, a_{_isNeList}, a_{_isList}, a_{_isQid}, a_{_isNePal}, a_{_isPal}, isNeList, isPalListKind, isQid, isList, isNePal, isPal]
a > [tt, a_{_{isPalListKind}}, a_{_isNeList}, a_{_isList}, a_{_isQid}, a_{_isNePal}, a_{_isPal}, isNeList, isPalListKind, isQid, isList, isNePal, isPal]

Status:

i: []
isPal: []
a_{_{_{_₂}}}: [1,2]
A_{_{_{_₂}}}: [1,2]
a: []
__₂: [1,2]
a_{_isQid}: []
e: []
isNeList: []
isPalListKind: []
a_{_isList}: []
a_{_isPal}: []
o: []
a_{_{isPalListKind}}: []
isList: []
tt: []
a_{_isNeList}: []
u: []
a_{_isNePal}: []
isNePal: []
isQid: []
nil: []

The following usable rules [FROCOS05] were oriented:

a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U46(tt) → tt
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U56(tt) → tt
a__U63(tt) → tt
a__U62(tt, V) → a__U63(a__isQid(V))
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isPalListKind(u) → tt
a__isPalListKind(o) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(i) → tt
a__isPalListKind(e) → tt
a__isPalListKind(a) → tt
a__isPal(nil) → tt
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
a__isQid(u) → tt
a__isQid(o) → tt
a__isQid(i) → tt
a__isQid(e) → tt
a__isQid(a) → tt
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U46(X)) → a__U46(mark(X))
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U63(X)) → a__U63(mark(X))
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__U62(X1, X2) → U62(X1, X2)
a__U61(X1, X2) → U61(X1, X2)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U63(X) → U63(X)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U56(X) → U56(X)
a__U55(X1, X2) → U55(X1, X2)
a__U46(X) → U46(X)
a__U45(X1, X2) → U45(X1, X2)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)

(22) Obligation:

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

MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(U11(X1, X2)) → MARK(X1)
MARK(U12(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(23) DependencyGraphProof (EQUIVALENT transformation)

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

(24) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U42(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(25) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U42(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U12(x1, x2) = x1
U11(x1, x2) = x1
U13(x1) = x1
U21(x1, x2, x3) = x1
U22(x1, x2, x3) = x1
U23(x1, x2, x3) = x1
U24(x1, x2, x3) = x1
U25(x1, x2) = x1
U26(x1) = x1
U31(x1, x2) = x1
U32(x1, x2) = x1
U33(x1) = x1
U41(x1, x2, x3) = x1
U42(x1, x2, x3) = U42(x1, x2, x3)
U43(x1, x2, x3) = x1
U44(x1, x2, x3) = x1
U45(x1, x2) = x1
U46(x1) = x1
U51(x1, x2, x3) = x1
U52(x1, x2, x3) = x1
U53(x1, x2, x3) = 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) = x1
U72(x1, x2) = x1
U73(x1, x2) = x1
U74(x1) = x1
U81(x1, x2) = x1
U82(x1, x2) = x1
U83(x1) = x1
U91(x1, x2) = x1
U92(x1) = x1

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

U42₃ > MARK₁

Status:

MARK₁: [1]
U42₃: [3,2,1]

The following usable rules [FROCOS05] were oriented: none

(26) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U81(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(27) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U21(X1, X2, X3)) → MARK(X1)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U45(X1, X2)) → MARK(X1)
MARK(U81(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U12(x1, x2) = x1
U11(x1, x2) = x1
U13(x1) = x1
U21(x1, x2, x3) = U21(x1, x2, x3)
U22(x1, x2, x3) = x1
U23(x1, x2, x3) = x1
U24(x1, x2, x3) = x1
U25(x1, x2) = x1
U26(x1) = x1
U31(x1, x2) = U31(x1, x2)
U32(x1, x2) = x1
U33(x1) = x1
U41(x1, x2, x3) = x1
U43(x1, x2, x3) = x1
U44(x1, x2, x3) = x1
U45(x1, x2) = U45(x1, x2)
U46(x1) = x1
U51(x1, x2, x3) = x1
U52(x1, x2, x3) = x1
U53(x1, x2, x3) = 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) = x1
U72(x1, x2) = x1
U73(x1, x2) = x1
U74(x1) = x1
U81(x1, x2) = U81(x1, x2)
U82(x1, x2) = x1
U83(x1) = x1
U91(x1, x2) = x1
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U31₂: [2,1]
U81₂: [2,1]
U45₂: [2,1]
U21₃: [2,3,1]

The following usable rules [FROCOS05] were oriented: none

(28) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(29) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U44(X1, X2, X3)) → MARK(X1)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U72(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U12(x1, x2) = x1
U11(x1, x2) = x1
U13(x1) = x1
U22(x1, x2, x3) = x1
U23(x1, x2, x3) = x1
U24(x1, x2, x3) = x1
U25(x1, x2) = x1
U26(x1) = x1
U32(x1, x2) = x1
U33(x1) = x1
U41(x1, x2, x3) = x1
U43(x1, x2, x3) = x1
U44(x1, x2, x3) = U44(x1)
U46(x1) = x1
U51(x1, x2, x3) = x1
U52(x1, x2, x3) = x1
U53(x1, x2, x3) = 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) = x1
U72(x1, x2) = U72(x1, x2)
U73(x1, x2) = x1
U74(x1) = x1
U82(x1, x2) = x1
U83(x1) = x1
U91(x1, x2) = x1
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U61₂: [2,1]
U72₂: [2,1]
U44₁: [1]

The following usable rules [FROCOS05] were oriented: none

(30) Obligation:

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

MARK(U12(X1, X2)) → MARK(X1)
MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(31) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U12(X1, X2)) → MARK(X1)
MARK(U52(X1, X2, X3)) → MARK(X1)
MARK(U53(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U12(x1, x2) = U12(x1, x2)
U11(x1, x2) = x1
U13(x1) = x1
U22(x1, x2, x3) = x1
U23(x1, x2, x3) = x1
U24(x1, x2, x3) = x1
U25(x1, x2) = x1
U26(x1) = x1
U32(x1, x2) = x1
U33(x1) = x1
U41(x1, x2, x3) = x1
U43(x1, x2, x3) = x1
U46(x1) = x1
U51(x1, x2, x3) = x1
U52(x1, x2, x3) = U52(x1, x2, x3)
U53(x1, x2, x3) = U53(x1, x2, x3)
U54(x1, x2, x3) = x1
U55(x1, x2) = x1
U56(x1) = x1
U62(x1, x2) = x1
U63(x1) = x1
U71(x1, x2, x3) = x1
U73(x1, x2) = x1
U74(x1) = x1
U82(x1, x2) = x1
U83(x1) = x1
U91(x1, x2) = x1
U92(x1) = x1

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

trivial

Status:

U52₃: [1,2,3]
MARK₁: [1]
U12₂: [1,2]
U53₃: [3,2,1]

The following usable rules [FROCOS05] were oriented: none

(32) Obligation:

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

MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(33) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U24(X1, X2, X3)) → MARK(X1)
MARK(U43(X1, X2, X3)) → MARK(X1)
MARK(U54(X1, X2, X3)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U11(x1, x2) = x1
U13(x1) = x1
U22(x1, x2, x3) = x1
U23(x1, x2, x3) = x1
U24(x1, x2, x3) = U24(x1, x2, x3)
U25(x1, x2) = x1
U26(x1) = x1
U32(x1, x2) = x1
U33(x1) = x1
U41(x1, x2, x3) = x1
U43(x1, x2, x3) = U43(x1, x2)
U46(x1) = x1
U51(x1, x2, x3) = x1
U54(x1, x2, x3) = U54(x1, x3)
U55(x1, x2) = x1
U56(x1) = x1
U62(x1, x2) = x1
U63(x1) = x1
U71(x1, x2, x3) = x1
U73(x1, x2) = x1
U74(x1) = x1
U82(x1, x2) = x1
U83(x1) = x1
U91(x1, x2) = x1
U92(x1) = x1

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

[MARK₁, U43₂]

Status:

MARK₁: [1]
U24₃: [3,2,1]
U43₂: [2,1]
U54₂: [2,1]

The following usable rules [FROCOS05] were oriented: none

(34) Obligation:

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

MARK(U11(X1, X2)) → MARK(X1)
MARK(U13(X)) → MARK(X)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U26(X)) → MARK(X)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U33(X)) → MARK(X)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U46(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U56(X)) → MARK(X)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U63(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U74(X)) → MARK(X)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U83(X)) → MARK(X)
MARK(U91(X1, X2)) → MARK(X1)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(35) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U11(X1, X2)) → MARK(X1)
MARK(U22(X1, X2, X3)) → MARK(X1)
MARK(U23(X1, X2, X3)) → MARK(X1)
MARK(U25(X1, X2)) → MARK(X1)
MARK(U32(X1, X2)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(U51(X1, X2, X3)) → MARK(X1)
MARK(U55(X1, X2)) → MARK(X1)
MARK(U62(X1, X2)) → MARK(X1)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U73(X1, X2)) → MARK(X1)
MARK(U82(X1, X2)) → MARK(X1)
MARK(U91(X1, X2)) → MARK(X1)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = x1
U11(x1, x2) = U11(x1, x2)
U13(x1) = x1
U22(x1, x2, x3) = U22(x1, x2, x3)
U23(x1, x2, x3) = U23(x1, x2, x3)
U25(x1, x2) = U25(x1, x2)
U26(x1) = x1
U32(x1, x2) = U32(x1, x2)
U33(x1) = x1
U41(x1, x2, x3) = U41(x1, x2, x3)
U46(x1) = x1
U51(x1, x2, x3) = U51(x1, x2, x3)
U55(x1, x2) = U55(x1, x2)
U56(x1) = x1
U62(x1, x2) = U62(x1, x2)
U63(x1) = x1
U71(x1, x2, x3) = U71(x1, x2, x3)
U73(x1, x2) = U73(x1, x2)
U74(x1) = x1
U82(x1, x2) = U82(x1, x2)
U83(x1) = x1
U91(x1, x2) = U91(x1, x2)
U92(x1) = x1

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

trivial

Status:

U91₂: [2,1]
U73₂: [2,1]
U62₂: [2,1]
U55₂: [2,1]
U41₃: [3,2,1]
U32₂: [2,1]
U25₂: [2,1]
U11₂: [2,1]
U23₃: [3,2,1]
U82₂: [2,1]
U22₃: [3,2,1]
U51₃: [3,2,1]
U71₃: [3,2,1]

The following usable rules [FROCOS05] were oriented: none

(36) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U26(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U46(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U83(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(37) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U46(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U13(x1) = x1
U26(x1) = x1
U33(x1) = x1
U46(x1) = U46(x1)
U56(x1) = x1
U63(x1) = x1
U74(x1) = x1
U83(x1) = x1
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U46₁: [1]

The following usable rules [FROCOS05] were oriented: none

(38) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U26(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U63(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U83(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(39) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U63(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U13(x1) = x1
U26(x1) = x1
U33(x1) = x1
U56(x1) = x1
U63(x1) = U63(x1)
U74(x1) = x1
U83(x1) = x1
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U63₁: [1]

The following usable rules [FROCOS05] were oriented: none

(40) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U26(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U74(X)) → MARK(X)
MARK(U83(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(41) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U74(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U13(x1) = x1
U26(x1) = x1
U33(x1) = x1
U56(x1) = x1
U74(x1) = U74(x1)
U83(x1) = x1
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U74₁: [1]

The following usable rules [FROCOS05] were oriented: none

(42) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U26(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U83(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(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.

MARK(U83(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U13(x1) = x1
U26(x1) = x1
U33(x1) = x1
U56(x1) = x1
U83(x1) = U83(x1)
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U83₁: [1]

The following usable rules [FROCOS05] were oriented: none

(44) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U26(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(45) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U26(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U13(x1) = x1
U26(x1) = U26(x1)
U33(x1) = x1
U56(x1) = x1
U92(x1) = x1

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

trivial

Status:

U26₁: [1]
MARK₁: [1]

The following usable rules [FROCOS05] were oriented: none

(46) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U33(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(47) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U33(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = x1
U13(x1) = x1
U33(x1) = U33(x1)
U56(x1) = x1
U92(x1) = x1

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

trivial

Status:

U33₁: [1]

The following usable rules [FROCOS05] were oriented: none

(48) Obligation:

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

MARK(U13(X)) → MARK(X)
MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(49) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U13(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = MARK(x1)
U13(x1) = U13(x1)
U56(x1) = x1
U92(x1) = x1

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

trivial

Status:

MARK₁: [1]
U13₁: [1]

The following usable rules [FROCOS05] were oriented: none

(50) Obligation:

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

MARK(U56(X)) → MARK(X)
MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(51) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U56(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = x1
U56(x1) = U56(x1)
U92(x1) = x1

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

trivial

Status:

U56₁: [1]

The following usable rules [FROCOS05] were oriented: none

(52) Obligation:

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

MARK(U92(X)) → MARK(X)

The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(53) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

MARK(U92(X)) → MARK(X)

The remaining pairs can at least be oriented weakly.
Used ordering: Combined order from the following AFS and order.
MARK(x1) = x1
U92(x1) = U92(x1)

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

trivial

Status:

U92₁: [1]

The following usable rules [FROCOS05] were oriented: none

(54) Obligation:

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

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

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

(55) PisEmptyProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) DependencyPairsProof (EQUIVALENT transformation)

(2) Obligation:

(3) DependencyGraphProof (EQUIVALENT transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) QDPOrderProof (EQUIVALENT transformation)

(7) Obligation:

(8) PisEmptyProof (EQUIVALENT transformation)

(9) TRUE

(10) Obligation:

(11) QDPOrderProof (EQUIVALENT transformation)

(12) Obligation:

(13) DependencyGraphProof (EQUIVALENT transformation)

(14) TRUE

(15) Obligation:

(16) QDPOrderProof (EQUIVALENT transformation)

(17) Obligation:

(18) DependencyGraphProof (EQUIVALENT transformation)

(19) TRUE

(20) Obligation:

(21) QDPOrderProof (EQUIVALENT transformation)

(22) Obligation:

(23) DependencyGraphProof (EQUIVALENT transformation)

(24) Obligation:

(25) QDPOrderProof (EQUIVALENT transformation)

(26) Obligation:

(27) QDPOrderProof (EQUIVALENT transformation)

(28) Obligation:

(29) QDPOrderProof (EQUIVALENT transformation)

(30) Obligation:

(31) QDPOrderProof (EQUIVALENT transformation)

(32) Obligation:

(33) QDPOrderProof (EQUIVALENT transformation)

(34) Obligation:

(35) QDPOrderProof (EQUIVALENT transformation)

(36) Obligation:

(37) QDPOrderProof (EQUIVALENT transformation)

(38) Obligation:

(39) QDPOrderProof (EQUIVALENT transformation)

(40) Obligation:

(41) QDPOrderProof (EQUIVALENT transformation)

(42) Obligation:

(43) QDPOrderProof (EQUIVALENT transformation)

(44) Obligation:

(45) QDPOrderProof (EQUIVALENT transformation)

(46) Obligation:

(47) QDPOrderProof (EQUIVALENT transformation)

(48) Obligation:

(49) QDPOrderProof (EQUIVALENT transformation)

(50) Obligation:

(51) QDPOrderProof (EQUIVALENT transformation)

(52) Obligation:

(53) QDPOrderProof (EQUIVALENT transformation)

(54) Obligation:

(55) PisEmptyProof (EQUIVALENT transformation)

(56) TRUE