TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60017 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (48354ms).
 | – Problem 2 was processed with processor DependencyGraph (9263ms).
 |    | – Problem 42 remains open; application of the following processors failed [].
 | – Problem 3 remains open; application of the following processors failed [SubtermCriterion (2ms), DependencyGraph (timeout)].
 | – Problem 4 remains open; application of the following processors failed [SubtermCriterion (4ms)].
 | – Problem 5 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 6 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 7 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 8 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 9 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 10 remains open; application of the following processors failed [SubtermCriterion (3ms)].
 | – Problem 11 remains open; application of the following processors failed [SubtermCriterion (3ms)].
 | – Problem 12 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 13 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 14 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 15 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 16 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 17 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 18 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 19 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 20 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 21 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 22 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 23 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 24 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 25 was processed with processor SubtermCriterion (2ms).
 |    | – Problem 40 remains open; application of the following processors failed [].
 | – Problem 26 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 27 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 28 remains open; application of the following processors failed [SubtermCriterion (5ms)].
 | – Problem 29 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 30 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 31 was processed with processor SubtermCriterion (3ms).
 |    | – Problem 41 remains open; application of the following processors failed [].
 | – Problem 32 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 33 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 34 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 35 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 36 remains open; application of the following processors failed [SubtermCriterion (2ms)].
 | – Problem 37 remains open; application of the following processors failed [SubtermCriterion (1ms)].
 | – Problem 38 remains open; application of the following processors failed [SubtermCriterion (3ms)].
 | – Problem 39 remains open; application of the following processors failed [SubtermCriterion (2ms)].

The following open problems remain:

Open Dependency Pair Problem 2

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U62(X1, X2)) → mark#(X1)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U52(X1, X2, X3)) → a__U52#(mark(X1), X2, X3)
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 3

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
a____#(__(X, Y), Z) → mark#(X)mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U33(X)) → a__U33#(mark(X))mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U52(X1, X2, X3)) → a__U52#(mark(X1), X2, X3)
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U25(X1, X2)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 4

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U61(X1, X2)) → mark#(X1)mark#(U45(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(isQid(X)) → a__isQid#(X)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U56(X)) → a__U56#(mark(X))
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 5

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U32(X1, X2)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U25(X1, X2)) → mark#(X1)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 6

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)
a____#(__(X, Y), Z) → mark#(X)mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U33(X)) → a__U33#(mark(X))mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 7

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 8

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 9

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U33(X)) → a__U33#(mark(X))mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U32(X1, X2)) → mark#(X1)mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U61(X1, X2)) → mark#(X1)
mark#(U45(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 10

Dependency Pairs

a__U52#(tt, V1, V2) → a__U53#(a__isPalListKind(V2), V1, V2)a__U54#(tt, V1, V2) → a__isNeList#(V1)
a__isList#(__(V1, V2)) → a__U21#(a__isPalListKind(V1), V1, V2)a__U21#(tt, V1, V2) → a__U22#(a__isPalListKind(V1), V1, V2)
a__isNeList#(__(V1, V2)) → a__U41#(a__isPalListKind(V1), V1, V2)a__U12#(tt, V) → a__isNeList#(V)
a__U25#(tt, V2) → a__isList#(V2)a__U24#(tt, V1, V2) → a__isList#(V1)
a__U11#(tt, V) → a__U12#(a__isPalListKind(V), V)a__U54#(tt, V1, V2) → a__U55#(a__isNeList(V1), V2)
a__U42#(tt, V1, V2) → a__U43#(a__isPalListKind(V2), V1, V2)a__U51#(tt, V1, V2) → a__U52#(a__isPalListKind(V1), V1, V2)
a__U22#(tt, V1, V2) → a__U23#(a__isPalListKind(V2), V1, V2)a__isNeList#(__(V1, V2)) → a__U51#(a__isPalListKind(V1), V1, V2)
a__U41#(tt, V1, V2) → a__U42#(a__isPalListKind(V1), V1, V2)a__U43#(tt, V1, V2) → a__U44#(a__isPalListKind(V2), V1, V2)
a__U45#(tt, V2) → a__isNeList#(V2)a__U24#(tt, V1, V2) → a__U25#(a__isList(V1), V2)
a__isList#(V) → a__U11#(a__isPalListKind(V), V)a__U53#(tt, V1, V2) → a__U54#(a__isPalListKind(V2), V1, V2)
a__U23#(tt, V1, V2) → a__U24#(a__isPalListKind(V2), V1, V2)a__U44#(tt, V1, V2) → a__isList#(V1)
a__U55#(tt, V2) → a__isList#(V2)a__U44#(tt, V1, V2) → a__U45#(a__isList(V1), V2)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 11

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U56(X)) → a__U56#(mark(X))
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 12

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)
a____#(__(X, Y), Z) → mark#(X)mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U33(X)) → a__U33#(mark(X))mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U74(X)) → mark#(X)mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 13

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U74(X)) → mark#(X)
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 14

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)
mark#(U32(X1, X2)) → mark#(X1)mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U61(X1, X2)) → mark#(X1)
mark#(U45(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(isNePal(X)) → a__isNePal#(X)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(isQid(X)) → a__isQid#(X)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 15

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))a____#(__(X, Y), Z) → mark#(X)
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U92(X)) → a__U92#(mark(X))
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U74(X)) → mark#(X)
mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U32(X1, X2)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → mark#(X1)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U25(X1, X2)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 17

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U74(X)) → mark#(X)
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 16

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)
mark#(__(X1, X2)) → mark#(X2)mark#(U81(X1, X2)) → a__U81#(mark(X1), X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U92(X)) → a__U92#(mark(X))
mark#(U74(X)) → mark#(X)mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(isQid(X)) → a__isQid#(X)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 19

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → a__U81#(mark(X1), X2)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U61(X1, X2)) → mark#(X1)mark#(U45(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U25(X1, X2)) → mark#(X1)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 18

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U32(X1, X2)) → mark#(X1)mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U52(X1, X2, X3)) → a__U52#(mark(X1), X2, X3)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 21

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(isQid(X)) → a__isQid#(X)
mark#(U56(X)) → mark#(X)mark#(U21(X1, X2, X3)) → a__U21#(mark(X1), X2, X3)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 20

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))mark#(U46(X)) → a__U46#(mark(X))
a____#(__(X, Y), Z) → mark#(X)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U61(X1, X2)) → mark#(X1)mark#(U45(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 23

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)
mark#(__(X1, X2)) → mark#(X2)mark#(U81(X1, X2)) → a__U81#(mark(X1), X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U92(X)) → a__U92#(mark(X))
mark#(U74(X)) → mark#(X)mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(isQid(X)) → a__isQid#(X)mark#(U56(X)) → mark#(X)
mark#(U21(X1, X2, X3)) → a__U21#(mark(X1), X2, X3)mark#(U25(X1, X2)) → mark#(X1)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 22

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))mark#(U46(X)) → a__U46#(mark(X))
a____#(__(X, Y), Z) → mark#(X)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)
mark#(U32(X1, X2)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 25

Dependency Pairs

a__U81#(tt, V) → a__U82#(a__isPalListKind(V), V)a__U82#(tt, V) → a__isNePal#(V)
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__isNePal#(__(I, __(P, I))) → a__U71#(a__isQid(I), I, P)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 24

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U74(X)) → mark#(X)
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 27

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))mark#(U46(X)) → a__U46#(mark(X))
a____#(__(X, Y), Z) → mark#(X)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U61(X1, X2)) → mark#(X1)mark#(U45(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U56(X)) → a__U56#(mark(X))
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 26

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U92(X)) → a__U92#(mark(X))
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)
mark#(U32(X1, X2)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U61(X1, X2)) → mark#(X1)
mark#(U45(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(isNePal(X)) → a__isNePal#(X)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 29

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
a____#(__(X, Y), Z) → mark#(X)mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U25(X1, X2)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 28

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U21(X1, X2, X3)) → a__U21#(mark(X1), X2, X3)mark#(U25(X1, X2)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 31

Dependency Pairs

a__isPalListKind#(__(V1, V2)) → a__U91#(a__isPalListKind(V1), V2)a__isPalListKind#(__(V1, V2)) → a__isPalListKind#(V1)
a__U91#(tt, V2) → a__isPalListKind#(V2)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 30

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
a____#(__(X, Y), Z) → mark#(X)mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 34

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))a____#(__(X, Y), Z) → mark#(X)
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U92(X)) → a__U92#(mark(X))
mark#(U74(X)) → mark#(X)mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U32(X1, X2)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(isNePal(X)) → a__isNePal#(X)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(U55(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → mark#(X1)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 35

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U61(X1, X2)) → mark#(X1)mark#(U45(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 32

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U32(X1, X2)) → mark#(X1)mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 33

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U74(X)) → mark#(X)
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → a__U42#(mark(X1), X2, X3)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U25(X1, X2)) → mark#(X1)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 38

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U33(X)) → a__U33#(mark(X))
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U74(X)) → mark#(X)
mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U32(X1, X2)) → mark#(X1)mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(U43(X1, X2, X3)) → mark#(X1)
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U55(X1, X2)) → mark#(X1)mark#(U62(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U52(X1, X2, X3)) → a__U52#(mark(X1), X2, X3)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(isPalListKind(X)) → a__isPalListKind#(X)mark#(U25(X1, X2)) → mark#(X1)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U56(X)) → a__U56#(mark(X))
mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 39

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)mark#(U54(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))a____#(__(X, Y), Z) → mark#(X)
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U33(X)) → a__U33#(mark(X))mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U32(X1, X2)) → mark#(X1)mark#(U26(X)) → a__U26#(mark(X))
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U26(X)) → mark#(X)
mark#(U82(X1, X2)) → mark#(X1)mark#(U56(X)) → mark#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)
mark#(U92(X)) → mark#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 36

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)
mark#(__(X1, X2)) → mark#(X2)mark#(U81(X1, X2)) → a__U81#(mark(X1), X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U52(X1, X2, X3)) → mark#(X1)mark#(U42(X1, X2, X3)) → mark#(X1)
mark#(U53(X1, X2, X3)) → mark#(X1)mark#(U92(X)) → a__U92#(mark(X))
mark#(U74(X)) → mark#(X)mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U32(X1, X2)) → mark#(X1)
mark#(U26(X)) → a__U26#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U45(X1, X2)) → mark#(X1)mark#(U61(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(U21(X1, X2, X3)) → a__U21#(mark(X1), X2, X3)
mark#(U25(X1, X2)) → mark#(X1)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(U73(X1, X2)) → mark#(X1)mark#(isNeList(X)) → a__isNeList#(X)
mark#(U43(X1, X2, X3)) → a__U43#(mark(X1), X2, X3)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Open Dependency Pair Problem 37

Dependency Pairs

mark#(U11(X1, X2)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Y)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(X)
mark#(U31(X1, X2)) → mark#(X1)mark#(__(X1, X2)) → mark#(X2)
mark#(U12(X1, X2)) → mark#(X1)mark#(U81(X1, X2)) → mark#(X1)
mark#(U72(X1, X2)) → mark#(X1)mark#(U71(X1, X2, X3)) → mark#(X1)
mark#(U33(X)) → a__U33#(mark(X))mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U92(X)) → a__U92#(mark(X))mark#(U74(X)) → mark#(X)
mark#(U82(X1, X2)) → a__U82#(mark(X1), X2)mark#(U41(X1, X2, X3)) → mark#(X1)
mark#(U63(X)) → mark#(X)mark#(U24(X1, X2, X3)) → mark#(X1)
mark#(U32(X1, X2)) → mark#(X1)mark#(U21(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X1)mark#(U46(X)) → mark#(X)
mark#(U61(X1, X2)) → mark#(X1)mark#(U45(X1, X2)) → mark#(X1)
mark#(U91(X1, X2)) → mark#(X1)mark#(isNePal(X)) → a__isNePal#(X)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))
mark#(U23(X1, X2, X3)) → mark#(X1)mark#(U55(X1, X2)) → mark#(X1)
mark#(U62(X1, X2)) → mark#(X1)a____#(nil, X) → mark#(X)
mark#(U33(X)) → mark#(X)a____#(X, nil) → mark#(X)
mark#(U44(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → mark#(Z)
mark#(U51(X1, X2, X3)) → mark#(X1)a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(isQid(X)) → a__isQid#(X)mark#(U56(X)) → mark#(X)
mark#(U25(X1, X2)) → mark#(X1)mark#(U22(X1, X2, X3)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → mark#(X1)
mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)mark#(U74(X)) → a__U74#(mark(X))
mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

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

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Strategy

The following SCCs where found

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

Problem 2: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a____#(__(X, Y), Z) → mark#(Y)mark#(U11(X1, X2)) → mark#(X1)
mark#(U83(X)) → mark#(X)a____#(__(X, Y), Z) → a____#(mark(Y), mark(Z))
mark#(U54(X1, X2, X3)) → mark#(X1)mark#(U46(X)) → a__U46#(mark(X))
mark#(U22(X1, X2, X3)) → a__U22#(mark(X1), X2, X3)a____#(__(X, Y), Z) → mark#(X)
mark#(U55(X1, X2)) → a__U55#(mark(X1), X2)mark#(U31(X1, X2)) → mark#(X1)
mark#(__(X1, X2)) → mark#(X2)mark#(U12(X1, X2)) → mark#(X1)
mark#(U81(X1, X2)) → mark#(X1)mark#(U72(X1, X2)) → mark#(X1)
mark#(U71(X1, X2, X3)) → mark#(X1)mark#(U52(X1, X2, X3)) → mark#(X1)
mark#(U42(X1, X2, X3)) → mark#(X1)mark#(U53(X1, X2, X3)) → mark#(X1)
mark#(U74(X)) → mark#(X)mark#(U71(X1, X2, X3)) → a__U71#(mark(X1), X2, X3)
mark#(U41(X1, X2, X3)) → mark#(X1)mark#(U63(X)) → mark#(X)
mark#(U24(X1, X2, X3)) → mark#(X1)mark#(U32(X1, X2)) → mark#(X1)
mark#(U21(X1, X2, X3)) → mark#(X1)mark#(__(X1, X2)) → mark#(X1)
mark#(U46(X)) → mark#(X)mark#(U45(X1, X2)) → mark#(X1)
mark#(U61(X1, X2)) → mark#(X1)mark#(U91(X1, X2)) → mark#(X1)
mark#(U43(X1, X2, X3)) → mark#(X1)mark#(U23(X1, X2, X3)) → mark#(X1)
mark#(__(X1, X2)) → a____#(mark(X1), mark(X2))mark#(U55(X1, X2)) → mark#(X1)
a____#(nil, X) → mark#(X)mark#(U62(X1, X2)) → a__U62#(mark(X1), X2)
mark#(U62(X1, X2)) → mark#(X1)mark#(U33(X)) → mark#(X)
a____#(X, nil) → mark#(X)mark#(U44(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → mark#(Z)mark#(U51(X1, X2, X3)) → mark#(X1)
a____#(__(X, Y), Z) → a____#(mark(X), a____(mark(Y), mark(Z)))mark#(U52(X1, X2, X3)) → a__U52#(mark(X1), X2, X3)
mark#(U26(X)) → mark#(X)mark#(U82(X1, X2)) → mark#(X1)
mark#(U56(X)) → mark#(X)mark#(isPalListKind(X)) → a__isPalListKind#(X)
mark#(U22(X1, X2, X3)) → mark#(X1)mark#(U25(X1, X2)) → mark#(X1)
mark#(U56(X)) → a__U56#(mark(X))mark#(U51(X1, X2, X3)) → a__U51#(mark(X1), X2, X3)
mark#(U53(X1, X2, X3)) → a__U53#(mark(X1), X2, X3)mark#(U92(X)) → mark#(X)
mark#(isNeList(X)) → a__isNeList#(X)mark#(U73(X1, X2)) → a__U73#(mark(X1), X2)
mark#(U73(X1, X2)) → mark#(X1)mark#(U11(X1, X2)) → a__U11#(mark(X1), X2)
mark#(U74(X)) → a__U74#(mark(X))mark#(U13(X)) → mark#(X)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Strategy

The following SCCs where found

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

Problem 25: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

a__U81#(tt, V) → a__U82#(a__isPalListKind(V), V)a__U82#(tt, V) → a__isNePal#(V)
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__isNePal#(__(I, __(P, I))) → a__U71#(a__isQid(I), I, P)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

a__isNePal#(__(I, __(P, I))) → a__U71#(a__isQid(I), I, P)

Problem 31: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

a__isPalListKind#(__(V1, V2)) → a__U91#(a__isPalListKind(V1), V2)a__isPalListKind#(__(V1, V2)) → a__isPalListKind#(V1)
a__U91#(tt, V2) → a__isPalListKind#(V2)

Rewrite 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) → tta__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) → tta__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) → tta__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) → tta__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tta__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tta__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) → tta__isPalListKind(a) → tt
a__isPalListKind(e) → tta__isPalListKind(i) → tt
a__isPalListKind(nil) → tta__isPalListKind(o) → tt
a__isPalListKind(u) → tta__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tta__isQid(e) → tt
a__isQid(i) → tta__isQid(o) → tt
a__isQid(u) → ttmark(__(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) → nilmark(tt) → tt
mark(a) → amark(e) → e
mark(i) → imark(o) → o
mark(u) → ua____(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)

Original Signature

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

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

a__isPalListKind#(__(V1, V2)) → a__U91#(a__isPalListKind(V1), V2)a__isPalListKind#(__(V1, V2)) → a__isPalListKind#(V1)