Runtime Complexity (full) proof of /tmp/tmpupIehc/PALINDROME_complete_noand

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

0 CpxTRS

↳1 NestedDefinedSymbolProof (BOTH BOUNDS(ID, ID), 10 ms)

↳2 CpxTRS

↳3 RcToIrcProof (BOTH BOUNDS(ID, ID), 133 ms)

↳4 CpxTRS

↳5 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID), 7 ms)

↳6 CdtProblem

↳7 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID), 0 ms)

↳8 CdtProblem

↳9 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 0 ms)

↳10 CdtProblem

↳11 CdtUsableRulesProof (⇔, 0 ms)

↳12 CdtProblem

↳13 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 367 ms)

↳14 CdtProblem

↳15 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 119 ms)

↳16 CdtProblem

↳17 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 92 ms)

↳18 CdtProblem

↳19 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 104 ms)

↳20 CdtProblem

↳21 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 88 ms)

↳22 CdtProblem

↳23 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 104 ms)

↳24 CdtProblem

↳25 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 76 ms)

↳26 CdtProblem

↳27 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 77 ms)

↳28 CdtProblem

↳29 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 81 ms)

↳30 CdtProblem

↳31 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 84 ms)

↳32 CdtProblem

↳33 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 84 ms)

↳34 CdtProblem

↳35 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 52 ms)

↳36 CdtProblem

↳37 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 59 ms)

↳38 CdtProblem

↳39 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 37 ms)

↳40 CdtProblem

↳41 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 65 ms)

↳42 CdtProblem

↳43 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 73 ms)

↳44 CdtProblem

↳45 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 64 ms)

↳46 CdtProblem

↳47 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 59 ms)

↳48 CdtProblem

↳49 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 80 ms)

↳50 CdtProblem

↳51 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 88 ms)

↳52 CdtProblem

↳53 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 55 ms)

↳54 CdtProblem

↳55 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 53 ms)

↳56 CdtProblem

↳57 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 30 ms)

↳58 CdtProblem

↳59 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 51 ms)

↳60 CdtProblem

↳61 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 22 ms)

↳62 CdtProblem

↳63 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 90 ms)

↳64 CdtProblem

↳65 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 36 ms)

↳66 CdtProblem

↳67 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 46 ms)

↳68 CdtProblem

↳69 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 50 ms)

↳70 CdtProblem

↳71 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 56 ms)

↳72 CdtProblem

↳73 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 44 ms)

↳74 CdtProblem

↳75 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 44 ms)

↳76 CdtProblem

↳77 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 29 ms)

↳78 CdtProblem

↳79 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 41 ms)

↳80 CdtProblem

↳81 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 17 ms)

↳82 CdtProblem

↳83 CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)), 54 ms)

↳84 CdtProblem

↳85 SIsEmptyProof (BOTH BOUNDS(ID, ID), 0 ms)

↳86 BOUNDS(1, 1)

(0) Obligation:

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

The TRS R consists of the following rules:

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

Rewrite Strategy: FULL

(1) NestedDefinedSymbolProof (BOTH BOUNDS(ID, ID) transformation)

The following defined symbols can occur below the 0th argument of top: proper, active
The following defined symbols can occur below the 0th argument of proper: proper, active
The following defined symbols can occur below the 0th argument of active: proper, active

Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(U11(tt, V)) → mark(U12(isPalListKind(V), V))
active(U12(tt, V)) → mark(U13(isNeList(V)))
active(U13(tt)) → mark(tt)
active(U21(tt, V1, V2)) → mark(U22(isPalListKind(V1), V1, V2))
active(U22(tt, V1, V2)) → mark(U23(isPalListKind(V2), V1, V2))
active(U23(tt, V1, V2)) → mark(U24(isPalListKind(V2), V1, V2))
active(U24(tt, V1, V2)) → mark(U25(isList(V1), V2))
active(U25(tt, V2)) → mark(U26(isList(V2)))
active(U26(tt)) → mark(tt)
active(U31(tt, V)) → mark(U32(isPalListKind(V), V))
active(U32(tt, V)) → mark(U33(isQid(V)))
active(U33(tt)) → mark(tt)
active(U41(tt, V1, V2)) → mark(U42(isPalListKind(V1), V1, V2))
active(U42(tt, V1, V2)) → mark(U43(isPalListKind(V2), V1, V2))
active(U43(tt, V1, V2)) → mark(U44(isPalListKind(V2), V1, V2))
active(U44(tt, V1, V2)) → mark(U45(isList(V1), V2))
active(U45(tt, V2)) → mark(U46(isNeList(V2)))
active(U46(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isPalListKind(V1), V1, V2))
active(U52(tt, V1, V2)) → mark(U53(isPalListKind(V2), V1, V2))
active(U53(tt, V1, V2)) → mark(U54(isPalListKind(V2), V1, V2))
active(U54(tt, V1, V2)) → mark(U55(isNeList(V1), V2))
active(U55(tt, V2)) → mark(U56(isList(V2)))
active(U56(tt)) → mark(tt)
active(U61(tt, V)) → mark(U62(isPalListKind(V), V))
active(U62(tt, V)) → mark(U63(isQid(V)))
active(U63(tt)) → mark(tt)
active(U71(tt, I, P)) → mark(U72(isPalListKind(I), P))
active(U72(tt, P)) → mark(U73(isPal(P), P))
active(U73(tt, P)) → mark(U74(isPalListKind(P)))
active(U74(tt)) → mark(tt)
active(U81(tt, V)) → mark(U82(isPalListKind(V), V))
active(U82(tt, V)) → mark(U83(isNePal(V)))
active(U83(tt)) → mark(tt)
active(U91(tt, V2)) → mark(U92(isPalListKind(V2)))
active(U92(tt)) → mark(tt)
active(isList(V)) → mark(U11(isPalListKind(V), V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(U21(isPalListKind(V1), V1, V2))
active(isNeList(V)) → mark(U31(isPalListKind(V), V))
active(isNeList(__(V1, V2))) → mark(U41(isPalListKind(V1), V1, V2))
active(isNeList(__(V1, V2))) → mark(U51(isPalListKind(V1), V1, V2))
active(isNePal(V)) → mark(U61(isPalListKind(V), V))
active(isNePal(__(I, __(P, I)))) → mark(U71(isQid(I), I, P))
active(isPal(V)) → mark(U81(isPalListKind(V), V))
active(isPal(nil)) → mark(tt)
active(isPalListKind(a)) → mark(tt)
active(isPalListKind(e)) → mark(tt)
active(isPalListKind(i)) → mark(tt)
active(isPalListKind(nil)) → mark(tt)
active(isPalListKind(o)) → mark(tt)
active(isPalListKind(u)) → mark(tt)
active(isPalListKind(__(V1, V2))) → mark(U91(isPalListKind(V1), V2))
active(isQid(a)) → mark(tt)
active(isQid(e)) → mark(tt)
active(isQid(i)) → mark(tt)
active(isQid(o)) → mark(tt)
active(isQid(u)) → mark(tt)
active(__(X1, X2)) → __(active(X1), X2)
active(__(X1, X2)) → __(X1, active(X2))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X1, X2)) → U12(active(X1), X2)
active(U13(X)) → U13(active(X))
active(U21(X1, X2, X3)) → U21(active(X1), X2, X3)
active(U22(X1, X2, X3)) → U22(active(X1), X2, X3)
active(U23(X1, X2, X3)) → U23(active(X1), X2, X3)
active(U24(X1, X2, X3)) → U24(active(X1), X2, X3)
active(U25(X1, X2)) → U25(active(X1), X2)
active(U26(X)) → U26(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X1, X2)) → U32(active(X1), X2)
active(U33(X)) → U33(active(X))
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3)
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3)
active(U43(X1, X2, X3)) → U43(active(X1), X2, X3)
active(U44(X1, X2, X3)) → U44(active(X1), X2, X3)
active(U45(X1, X2)) → U45(active(X1), X2)
active(U46(X)) → U46(active(X))
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(U53(X1, X2, X3)) → U53(active(X1), X2, X3)
active(U54(X1, X2, X3)) → U54(active(X1), X2, X3)
active(U55(X1, X2)) → U55(active(X1), X2)
active(U56(X)) → U56(active(X))
active(U61(X1, X2)) → U61(active(X1), X2)
active(U62(X1, X2)) → U62(active(X1), X2)
active(U63(X)) → U63(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2)) → U72(active(X1), X2)
active(U73(X1, X2)) → U73(active(X1), X2)
active(U74(X)) → U74(active(X))
active(U81(X1, X2)) → U81(active(X1), X2)
active(U82(X1, X2)) → U82(active(X1), X2)
active(U83(X)) → U83(active(X))
active(U91(X1, X2)) → U91(active(X1), X2)
active(U92(X)) → U92(active(X))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(U12(X1, X2)) → U12(proper(X1), proper(X2))
proper(isPalListKind(X)) → isPalListKind(proper(X))
proper(U13(X)) → U13(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(U21(X1, X2, X3)) → U21(proper(X1), proper(X2), proper(X3))
proper(U22(X1, X2, X3)) → U22(proper(X1), proper(X2), proper(X3))
proper(U23(X1, X2, X3)) → U23(proper(X1), proper(X2), proper(X3))
proper(U24(X1, X2, X3)) → U24(proper(X1), proper(X2), proper(X3))
proper(U25(X1, X2)) → U25(proper(X1), proper(X2))
proper(isList(X)) → isList(proper(X))
proper(U26(X)) → U26(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X1, X2)) → U32(proper(X1), proper(X2))
proper(U33(X)) → U33(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3))
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3))
proper(U43(X1, X2, X3)) → U43(proper(X1), proper(X2), proper(X3))
proper(U44(X1, X2, X3)) → U44(proper(X1), proper(X2), proper(X3))
proper(U45(X1, X2)) → U45(proper(X1), proper(X2))
proper(U46(X)) → U46(proper(X))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(U53(X1, X2, X3)) → U53(proper(X1), proper(X2), proper(X3))
proper(U54(X1, X2, X3)) → U54(proper(X1), proper(X2), proper(X3))
proper(U55(X1, X2)) → U55(proper(X1), proper(X2))
proper(U56(X)) → U56(proper(X))
proper(U61(X1, X2)) → U61(proper(X1), proper(X2))
proper(U62(X1, X2)) → U62(proper(X1), proper(X2))
proper(U63(X)) → U63(proper(X))
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2)) → U72(proper(X1), proper(X2))
proper(U73(X1, X2)) → U73(proper(X1), proper(X2))
proper(isPal(X)) → isPal(proper(X))
proper(U74(X)) → U74(proper(X))
proper(U81(X1, X2)) → U81(proper(X1), proper(X2))
proper(U82(X1, X2)) → U82(proper(X1), proper(X2))
proper(U83(X)) → U83(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(U91(X1, X2)) → U91(proper(X1), proper(X2))
proper(U92(X)) → U92(proper(X))

(2) Obligation:

The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

The TRS R consists of the following rules:

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

Rewrite Strategy: FULL

(3) RcToIrcProof (BOTH BOUNDS(ID, ID) transformation)

Converted rc-obligation to irc-obligation.

As the TRS is a non-duplicating overlay system, we have rc = irc.

(4) Obligation:

The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).

The TRS R consists of the following rules:

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

Rewrite Strategy: INNERMOST

(5) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted Cpx (relative) TRS to CDT

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
top(ok(z0)) → top(active(z0))
top(mark(z0)) → top(proper(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
U32(mark(z0), z1) → mark(U32(z0, z1))
U32(ok(z0), ok(z1)) → ok(U32(z0, z1))
U91(mark(z0), z1) → mark(U91(z0, z1))
U91(ok(z0), ok(z1)) → ok(U91(z0, z1))
U43(ok(z0), ok(z1), ok(z2)) → ok(U43(z0, z1, z2))
U43(mark(z0), z1, z2) → mark(U43(z0, z1, z2))
U26(ok(z0)) → ok(U26(z0))
U26(mark(z0)) → mark(U26(z0))
U82(mark(z0), z1) → mark(U82(z0, z1))
U82(ok(z0), ok(z1)) → ok(U82(z0, z1))
U61(ok(z0), ok(z1)) → ok(U61(z0, z1))
U61(mark(z0), z1) → mark(U61(z0, z1))
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2))
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2))
U33(mark(z0)) → mark(U33(z0))
U33(ok(z0)) → ok(U33(z0))
U92(mark(z0)) → mark(U92(z0))
U92(ok(z0)) → ok(U92(z0))
proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
__(z0, mark(z1)) → mark(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
U73(ok(z0), ok(z1)) → ok(U73(z0, z1))
U73(mark(z0), z1) → mark(U73(z0, z1))
U63(mark(z0)) → mark(U63(z0))
U63(ok(z0)) → ok(U63(z0))
U62(mark(z0), z1) → mark(U62(z0, z1))
U62(ok(z0), ok(z1)) → ok(U62(z0, z1))
U83(mark(z0)) → mark(U83(z0))
U83(ok(z0)) → ok(U83(z0))
U23(ok(z0), ok(z1), ok(z2)) → ok(U23(z0, z1, z2))
U23(mark(z0), z1, z2) → mark(U23(z0, z1, z2))
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2))
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2))
U55(ok(z0), ok(z1)) → ok(U55(z0, z1))
U55(mark(z0), z1) → mark(U55(z0, z1))
U45(mark(z0), z1) → mark(U45(z0, z1))
U45(ok(z0), ok(z1)) → ok(U45(z0, z1))
isPal(ok(z0)) → ok(isPal(z0))
U13(mark(z0)) → mark(U13(z0))
U13(ok(z0)) → ok(U13(z0))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U56(mark(z0)) → mark(U56(z0))
U56(ok(z0)) → ok(U56(z0))
U46(ok(z0)) → ok(U46(z0))
U46(mark(z0)) → mark(U46(z0))
U74(mark(z0)) → mark(U74(z0))
U74(ok(z0)) → ok(U74(z0))
U53(ok(z0), ok(z1), ok(z2)) → ok(U53(z0, z1, z2))
U53(mark(z0), z1, z2) → mark(U53(z0, z1, z2))
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2))
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2))
U25(mark(z0), z1) → mark(U25(z0, z1))
U25(ok(z0), ok(z1)) → ok(U25(z0, z1))
U24(ok(z0), ok(z1), ok(z2)) → ok(U24(z0, z1, z2))
U24(mark(z0), z1, z2) → mark(U24(z0, z1, z2))
isQid(ok(z0)) → ok(isQid(z0))
U72(mark(z0), z1) → mark(U72(z0, z1))
U72(ok(z0), ok(z1)) → ok(U72(z0, z1))
isNePal(ok(z0)) → ok(isNePal(z0))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U44(mark(z0), z1, z2) → mark(U44(z0, z1, z2))
U44(ok(z0), ok(z1), ok(z2)) → ok(U44(z0, z1, z2))
isList(ok(z0)) → ok(isList(z0))
U81(ok(z0), ok(z1)) → ok(U81(z0, z1))
U81(mark(z0), z1) → mark(U81(z0, z1))
isPalListKind(ok(z0)) → ok(isPalListKind(z0))
U54(mark(z0), z1, z2) → mark(U54(z0, z1, z2))
U54(ok(z0), ok(z1), ok(z2)) → ok(U54(z0, z1, z2))
U12(ok(z0), ok(z1)) → ok(U12(z0, z1))
U12(mark(z0), z1) → mark(U12(z0, z1))
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2))
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2))

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
TOP(ok(z0)) → c2(TOP(active(z0)))
TOP(mark(z0)) → c3(TOP(proper(z0)), PROPER(z0))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
PROPER(i) → c23
PROPER(u) → c24
PROPER(nil) → c25
PROPER(tt) → c26
PROPER(o) → c27
PROPER(e) → c28
PROPER(a) → c29
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
TOP(ok(z0)) → c2(TOP(active(z0)))
TOP(mark(z0)) → c3(TOP(proper(z0)), PROPER(z0))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
PROPER(i) → c23
PROPER(u) → c24
PROPER(nil) → c25
PROPER(tt) → c26
PROPER(o) → c27
PROPER(e) → c28
PROPER(a) → c29
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:none
Defined Rule Symbols:

U11, top, isNeList, U32, U91, U43, U26, U82, U61, U22, U33, U92, proper, U52, U51, __, U73, U63, U62, U83, U23, U42, U55, U45, isPal, U13, U31, U56, U46, U74, U53, U21, U25, U24, isQid, U72, isNePal, U71, U44, isList, U81, isPalListKind, U54, U12, U41

Defined Pair Symbols:

U11', TOP, ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', PROPER, U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41'

Compound Symbols:

c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89

(7) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 8 trailing nodes:

PROPER(u) → c24
PROPER(nil) → c25
PROPER(tt) → c26
PROPER(e) → c28
TOP(ok(z0)) → c2(TOP(active(z0)))
PROPER(o) → c27
PROPER(i) → c23
PROPER(a) → c29

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
top(ok(z0)) → top(active(z0))
top(mark(z0)) → top(proper(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
U32(mark(z0), z1) → mark(U32(z0, z1))
U32(ok(z0), ok(z1)) → ok(U32(z0, z1))
U91(mark(z0), z1) → mark(U91(z0, z1))
U91(ok(z0), ok(z1)) → ok(U91(z0, z1))
U43(ok(z0), ok(z1), ok(z2)) → ok(U43(z0, z1, z2))
U43(mark(z0), z1, z2) → mark(U43(z0, z1, z2))
U26(ok(z0)) → ok(U26(z0))
U26(mark(z0)) → mark(U26(z0))
U82(mark(z0), z1) → mark(U82(z0, z1))
U82(ok(z0), ok(z1)) → ok(U82(z0, z1))
U61(ok(z0), ok(z1)) → ok(U61(z0, z1))
U61(mark(z0), z1) → mark(U61(z0, z1))
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2))
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2))
U33(mark(z0)) → mark(U33(z0))
U33(ok(z0)) → ok(U33(z0))
U92(mark(z0)) → mark(U92(z0))
U92(ok(z0)) → ok(U92(z0))
proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
__(z0, mark(z1)) → mark(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
U73(ok(z0), ok(z1)) → ok(U73(z0, z1))
U73(mark(z0), z1) → mark(U73(z0, z1))
U63(mark(z0)) → mark(U63(z0))
U63(ok(z0)) → ok(U63(z0))
U62(mark(z0), z1) → mark(U62(z0, z1))
U62(ok(z0), ok(z1)) → ok(U62(z0, z1))
U83(mark(z0)) → mark(U83(z0))
U83(ok(z0)) → ok(U83(z0))
U23(ok(z0), ok(z1), ok(z2)) → ok(U23(z0, z1, z2))
U23(mark(z0), z1, z2) → mark(U23(z0, z1, z2))
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2))
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2))
U55(ok(z0), ok(z1)) → ok(U55(z0, z1))
U55(mark(z0), z1) → mark(U55(z0, z1))
U45(mark(z0), z1) → mark(U45(z0, z1))
U45(ok(z0), ok(z1)) → ok(U45(z0, z1))
isPal(ok(z0)) → ok(isPal(z0))
U13(mark(z0)) → mark(U13(z0))
U13(ok(z0)) → ok(U13(z0))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U56(mark(z0)) → mark(U56(z0))
U56(ok(z0)) → ok(U56(z0))
U46(ok(z0)) → ok(U46(z0))
U46(mark(z0)) → mark(U46(z0))
U74(mark(z0)) → mark(U74(z0))
U74(ok(z0)) → ok(U74(z0))
U53(ok(z0), ok(z1), ok(z2)) → ok(U53(z0, z1, z2))
U53(mark(z0), z1, z2) → mark(U53(z0, z1, z2))
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2))
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2))
U25(mark(z0), z1) → mark(U25(z0, z1))
U25(ok(z0), ok(z1)) → ok(U25(z0, z1))
U24(ok(z0), ok(z1), ok(z2)) → ok(U24(z0, z1, z2))
U24(mark(z0), z1, z2) → mark(U24(z0, z1, z2))
isQid(ok(z0)) → ok(isQid(z0))
U72(mark(z0), z1) → mark(U72(z0, z1))
U72(ok(z0), ok(z1)) → ok(U72(z0, z1))
isNePal(ok(z0)) → ok(isNePal(z0))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U44(mark(z0), z1, z2) → mark(U44(z0, z1, z2))
U44(ok(z0), ok(z1), ok(z2)) → ok(U44(z0, z1, z2))
isList(ok(z0)) → ok(isList(z0))
U81(ok(z0), ok(z1)) → ok(U81(z0, z1))
U81(mark(z0), z1) → mark(U81(z0, z1))
isPalListKind(ok(z0)) → ok(isPalListKind(z0))
U54(mark(z0), z1, z2) → mark(U54(z0, z1, z2))
U54(ok(z0), ok(z1), ok(z2)) → ok(U54(z0, z1, z2))
U12(ok(z0), ok(z1)) → ok(U12(z0, z1))
U12(mark(z0), z1) → mark(U12(z0, z1))
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2))
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2))

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
TOP(mark(z0)) → c3(TOP(proper(z0)), PROPER(z0))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
TOP(mark(z0)) → c3(TOP(proper(z0)), PROPER(z0))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:none
Defined Rule Symbols:

U11, top, isNeList, U32, U91, U43, U26, U82, U61, U22, U33, U92, proper, U52, U51, __, U73, U63, U62, U83, U23, U42, U55, U45, isPal, U13, U31, U56, U46, U74, U53, U21, U25, U24, isQid, U72, isNePal, U71, U44, isList, U81, isPalListKind, U54, U12, U41

Defined Pair Symbols:

U11', TOP, ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41'

Compound Symbols:

c, c1, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89

(9) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 1 trailing tuple parts

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
top(ok(z0)) → top(active(z0))
top(mark(z0)) → top(proper(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
U32(mark(z0), z1) → mark(U32(z0, z1))
U32(ok(z0), ok(z1)) → ok(U32(z0, z1))
U91(mark(z0), z1) → mark(U91(z0, z1))
U91(ok(z0), ok(z1)) → ok(U91(z0, z1))
U43(ok(z0), ok(z1), ok(z2)) → ok(U43(z0, z1, z2))
U43(mark(z0), z1, z2) → mark(U43(z0, z1, z2))
U26(ok(z0)) → ok(U26(z0))
U26(mark(z0)) → mark(U26(z0))
U82(mark(z0), z1) → mark(U82(z0, z1))
U82(ok(z0), ok(z1)) → ok(U82(z0, z1))
U61(ok(z0), ok(z1)) → ok(U61(z0, z1))
U61(mark(z0), z1) → mark(U61(z0, z1))
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2))
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2))
U33(mark(z0)) → mark(U33(z0))
U33(ok(z0)) → ok(U33(z0))
U92(mark(z0)) → mark(U92(z0))
U92(ok(z0)) → ok(U92(z0))
proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
__(z0, mark(z1)) → mark(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
U73(ok(z0), ok(z1)) → ok(U73(z0, z1))
U73(mark(z0), z1) → mark(U73(z0, z1))
U63(mark(z0)) → mark(U63(z0))
U63(ok(z0)) → ok(U63(z0))
U62(mark(z0), z1) → mark(U62(z0, z1))
U62(ok(z0), ok(z1)) → ok(U62(z0, z1))
U83(mark(z0)) → mark(U83(z0))
U83(ok(z0)) → ok(U83(z0))
U23(ok(z0), ok(z1), ok(z2)) → ok(U23(z0, z1, z2))
U23(mark(z0), z1, z2) → mark(U23(z0, z1, z2))
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2))
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2))
U55(ok(z0), ok(z1)) → ok(U55(z0, z1))
U55(mark(z0), z1) → mark(U55(z0, z1))
U45(mark(z0), z1) → mark(U45(z0, z1))
U45(ok(z0), ok(z1)) → ok(U45(z0, z1))
isPal(ok(z0)) → ok(isPal(z0))
U13(mark(z0)) → mark(U13(z0))
U13(ok(z0)) → ok(U13(z0))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U56(mark(z0)) → mark(U56(z0))
U56(ok(z0)) → ok(U56(z0))
U46(ok(z0)) → ok(U46(z0))
U46(mark(z0)) → mark(U46(z0))
U74(mark(z0)) → mark(U74(z0))
U74(ok(z0)) → ok(U74(z0))
U53(ok(z0), ok(z1), ok(z2)) → ok(U53(z0, z1, z2))
U53(mark(z0), z1, z2) → mark(U53(z0, z1, z2))
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2))
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2))
U25(mark(z0), z1) → mark(U25(z0, z1))
U25(ok(z0), ok(z1)) → ok(U25(z0, z1))
U24(ok(z0), ok(z1), ok(z2)) → ok(U24(z0, z1, z2))
U24(mark(z0), z1, z2) → mark(U24(z0, z1, z2))
isQid(ok(z0)) → ok(isQid(z0))
U72(mark(z0), z1) → mark(U72(z0, z1))
U72(ok(z0), ok(z1)) → ok(U72(z0, z1))
isNePal(ok(z0)) → ok(isNePal(z0))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U44(mark(z0), z1, z2) → mark(U44(z0, z1, z2))
U44(ok(z0), ok(z1), ok(z2)) → ok(U44(z0, z1, z2))
isList(ok(z0)) → ok(isList(z0))
U81(ok(z0), ok(z1)) → ok(U81(z0, z1))
U81(mark(z0), z1) → mark(U81(z0, z1))
isPalListKind(ok(z0)) → ok(isPalListKind(z0))
U54(mark(z0), z1, z2) → mark(U54(z0, z1, z2))
U54(ok(z0), ok(z1), ok(z2)) → ok(U54(z0, z1, z2))
U12(ok(z0), ok(z1)) → ok(U12(z0, z1))
U12(mark(z0), z1) → mark(U12(z0, z1))
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2))
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2))

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

K tuples:none
Defined Rule Symbols:

U11, top, isNeList, U32, U91, U43, U26, U82, U61, U22, U33, U92, proper, U52, U51, __, U73, U63, U62, U83, U23, U42, U55, U45, isPal, U13, U31, U56, U46, U74, U53, U21, U25, U24, isQid, U72, isNePal, U71, U44, isList, U81, isPalListKind, U54, U12, U41

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(11) CdtUsableRulesProof (EQUIVALENT transformation)

The following rules are not usable and were removed:

U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
top(ok(z0)) → top(active(z0))
top(mark(z0)) → top(proper(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
U32(mark(z0), z1) → mark(U32(z0, z1))
U32(ok(z0), ok(z1)) → ok(U32(z0, z1))
U91(mark(z0), z1) → mark(U91(z0, z1))
U91(ok(z0), ok(z1)) → ok(U91(z0, z1))
U43(ok(z0), ok(z1), ok(z2)) → ok(U43(z0, z1, z2))
U43(mark(z0), z1, z2) → mark(U43(z0, z1, z2))
U26(ok(z0)) → ok(U26(z0))
U26(mark(z0)) → mark(U26(z0))
U82(mark(z0), z1) → mark(U82(z0, z1))
U82(ok(z0), ok(z1)) → ok(U82(z0, z1))
U61(ok(z0), ok(z1)) → ok(U61(z0, z1))
U61(mark(z0), z1) → mark(U61(z0, z1))
U22(ok(z0), ok(z1), ok(z2)) → ok(U22(z0, z1, z2))
U22(mark(z0), z1, z2) → mark(U22(z0, z1, z2))
U33(mark(z0)) → mark(U33(z0))
U33(ok(z0)) → ok(U33(z0))
U92(mark(z0)) → mark(U92(z0))
U92(ok(z0)) → ok(U92(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
__(z0, mark(z1)) → mark(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
U73(ok(z0), ok(z1)) → ok(U73(z0, z1))
U73(mark(z0), z1) → mark(U73(z0, z1))
U63(mark(z0)) → mark(U63(z0))
U63(ok(z0)) → ok(U63(z0))
U62(mark(z0), z1) → mark(U62(z0, z1))
U62(ok(z0), ok(z1)) → ok(U62(z0, z1))
U83(mark(z0)) → mark(U83(z0))
U83(ok(z0)) → ok(U83(z0))
U23(ok(z0), ok(z1), ok(z2)) → ok(U23(z0, z1, z2))
U23(mark(z0), z1, z2) → mark(U23(z0, z1, z2))
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2))
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2))
U55(ok(z0), ok(z1)) → ok(U55(z0, z1))
U55(mark(z0), z1) → mark(U55(z0, z1))
U45(mark(z0), z1) → mark(U45(z0, z1))
U45(ok(z0), ok(z1)) → ok(U45(z0, z1))
isPal(ok(z0)) → ok(isPal(z0))
U13(mark(z0)) → mark(U13(z0))
U13(ok(z0)) → ok(U13(z0))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U56(mark(z0)) → mark(U56(z0))
U56(ok(z0)) → ok(U56(z0))
U46(ok(z0)) → ok(U46(z0))
U46(mark(z0)) → mark(U46(z0))
U74(mark(z0)) → mark(U74(z0))
U74(ok(z0)) → ok(U74(z0))
U53(ok(z0), ok(z1), ok(z2)) → ok(U53(z0, z1, z2))
U53(mark(z0), z1, z2) → mark(U53(z0, z1, z2))
U21(ok(z0), ok(z1), ok(z2)) → ok(U21(z0, z1, z2))
U21(mark(z0), z1, z2) → mark(U21(z0, z1, z2))
U25(mark(z0), z1) → mark(U25(z0, z1))
U25(ok(z0), ok(z1)) → ok(U25(z0, z1))
U24(ok(z0), ok(z1), ok(z2)) → ok(U24(z0, z1, z2))
U24(mark(z0), z1, z2) → mark(U24(z0, z1, z2))
isQid(ok(z0)) → ok(isQid(z0))
U72(mark(z0), z1) → mark(U72(z0, z1))
U72(ok(z0), ok(z1)) → ok(U72(z0, z1))
isNePal(ok(z0)) → ok(isNePal(z0))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U44(mark(z0), z1, z2) → mark(U44(z0, z1, z2))
U44(ok(z0), ok(z1), ok(z2)) → ok(U44(z0, z1, z2))
isList(ok(z0)) → ok(isList(z0))
U81(ok(z0), ok(z1)) → ok(U81(z0, z1))
U81(mark(z0), z1) → mark(U81(z0, z1))
isPalListKind(ok(z0)) → ok(isPalListKind(z0))
U54(mark(z0), z1, z2) → mark(U54(z0, z1, z2))
U54(ok(z0), ok(z1), ok(z2)) → ok(U54(z0, z1, z2))
U12(ok(z0), ok(z1)) → ok(U12(z0, z1))
U12(mark(z0), z1) → mark(U12(z0, z1))
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2))
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2))

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

K tuples:none
Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(13) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

TOP(mark(z0)) → c3(TOP(proper(z0)))

We considered the (Usable) Rules:

proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(u) → ok(u)
proper(e) → ok(e)
proper(a) → ok(a)
proper(i) → ok(i)

And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = x₁
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = 0
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(15) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = x₁
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = x₁
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₂
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = x₁
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = x₂
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₃
POL(U53'(x₁, x₂, x₃)) = x₁
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = x₁ + x₂
POL(U63'(x₁)) = x₁
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = x₁ + x₂
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = x₂
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = x₂
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = x₁
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(17) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = x₁
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = x₁ + x₃
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(19) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₁
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = x₁
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = x₁
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(21) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U45'(mark(z0), z1) → c51(U45'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = x₁
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = x₁
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = x₁
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = x₁
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = x₁
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(23) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = x₁
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = x₁
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = x₂
POL(U12'(x₁, x₂)) = x₂
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = x₂
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₂
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = x₂
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = [2]x₂
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = [2]x₂
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = [2]x₂
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = x₂
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = 0
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(mark(z0), z1) → c1(U11'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(25) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = x₁
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = x₁ + x₂
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(mark(z0), z1) → c1(U11'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(27) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = x₁
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = x₂
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₃
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = x₁
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₂ + x₃
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U11'(mark(z0), z1) → c1(U11'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(29) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U11'(mark(z0), z1) → c1(U11'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = x₁
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = x₁
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₂
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = x₂
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(31) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₂
POL(U22'(x₁, x₂, x₃)) = x₁
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = x₃
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₃
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = x₁
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = x₂
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = [1]
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = [1]
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = [1]
POL(ok(x₁)) = x₁
POL(proper(x₁)) = [1]
POL(tt) = 0
POL(u) = [1]

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(33) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₁
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = x₃
POL(U45'(x₁, x₂)) = x₂
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = x₂
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = x₁
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = x₂
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(35) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = x₁
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = x₂
POL(U13'(x₁)) = x₁
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = x₁
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = x₁
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = x₂
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = x₁
POL(U83'(x₁)) = x₁
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(37) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U12'(mark(z0), z1) → c87(U12'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = x₁
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = x₁
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₂
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = x₂
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₃
POL(U53'(x₁, x₂, x₃)) = x₃
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = x₁
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = x₁
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = x₁
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(39) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U61'(mark(z0), z1) → c16(U61'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = x₁
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = x₂
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₃
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = x₁
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = x₁
POL(U62'(x₁, x₂)) = x₂
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = x₂
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(41) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U46'(mark(z0)) → c61(U46'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = x₁
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(43) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = x₁
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(45) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U74'(mark(z0)) → c62(U74'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = x₁
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(47) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = x₂
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = x₁
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = x₂
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(49) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = x₁
POL(ISQID(x₁)) = [3]x₁
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = x₂ + x₃
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = [2]x₃
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = x₃
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = [2]x₃
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = [2]x₂
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = 0
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(51) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₃
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = x₁
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(53) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = x₂
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = x₃
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₁
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = x₂
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = x₁
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(55) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = x₁
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₃
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₁
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = x₂
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(57) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U91'(mark(z0), z1) → c7(U91'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = x₃
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = x₃
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = x₁
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(59) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = x₁
POL(U42'(x₁, x₂, x₃)) = x₂
POL(U43'(x₁, x₂, x₃)) = x₂
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = x₂
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = x₁
POL(__'(x₁, x₂)) = 0
POL(a) = [1]
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = [1]
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = [1] + x₁
POL(tt) = [1]
POL(u) = 0

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(61) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U56'(mark(z0)) → c58(U56'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = x₁ + x₂
POL(U56'(x₁)) = x₁
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = x₂
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(63) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = [2]x₁
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = [2]x₂
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = [3]x₂
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = [2]x₂
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = [2]x₂ + [2]x₃
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = [2]x₃
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = [2]x₂
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = [2]x₂
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = 0
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [2] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(65) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = x₁
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = x₁ + x₃
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = x₁
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = x₁
POL(U51'(x₁, x₂, x₃)) = x₂ + x₃
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = x₂
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(67) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = x₂
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₂
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = x₁
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = x₁
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = x₂ + x₃
POL(U54'(x₁, x₂, x₃)) = x₂
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = x₁
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = x₂
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = x₂
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(69) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = x₃
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = x₂
POL(U54'(x₁, x₂, x₃)) = x₁
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = x₂
POL(U73'(x₁, x₂)) = x₁
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(71) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = x₃
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = x₁
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = x₃
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = x₁
POL(U81'(x₁, x₂)) = x₁ + x₂
POL(U82'(x₁, x₂)) = x₂
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(73) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = x₁
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = x₂
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₃
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₂
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = x₂ + x₃
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = x₂ + x₃
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = 0
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U83'(ok(z0)) → c44(U83'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(75) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U83'(ok(z0)) → c44(U83'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = x₃
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₂
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = x₃
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = x₂
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = x₁
POL(U61'(x₁, x₂)) = x₂
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = x₃
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = x₂
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = x₁
POL(U83'(x₁)) = x₁
POL(U91'(x₁, x₂)) = x₂
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(77) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = [2]x₁
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = [2]x₁
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = [2]x₂
POL(U12'(x₁, x₂)) = [2]x₂
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = [2]x₂ + [2]x₃
POL(U24'(x₁, x₂, x₃)) = [2]x₃
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = x₂
POL(U32'(x₁, x₂)) = x₂
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = [2]x₂
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = [2]x₂
POL(U52'(x₁, x₂, x₃)) = [2]x₂
POL(U53'(x₁, x₂, x₃)) = [2]x₃
POL(U54'(x₁, x₂, x₃)) = [2]x₃
POL(U55'(x₁, x₂)) = [2]x₂
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = [2]x₂ + [2]x₃
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = [2]x₂
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = [2]x₂
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = 0
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [2] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U33'(ok(z0)) → c20(U33'(z0))
U92'(ok(z0)) → c22(U92'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(ok(z0)) → c55(U13'(z0))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(79) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U33'(ok(z0)) → c20(U33'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = x₁
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = x₁
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = x₁
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = 0
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U92'(ok(z0)) → c22(U92'(z0))
U13'(ok(z0)) → c55(U13'(z0))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(81) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U92'(ok(z0)) → c22(U92'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = 0
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = x₁
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = 0
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = 0
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = x₂ + x₃
POL(U52'(x₁, x₂, x₃)) = 0
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = 0
POL(U55'(x₁, x₂)) = 0
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = x₂
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = 0
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = x₁
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:

U13'(ok(z0)) → c55(U13'(z0))

K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U92'(ok(z0)) → c22(U92'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(83) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

U13'(ok(z0)) → c55(U13'(z0))

We considered the (Usable) Rules:none
And the Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

The order we found is given by the following interpretation:
Polynomial interpretation :

POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = x₁
POL(ISNEPAL(x₁)) = [2]x₁
POL(ISPAL(x₁)) = [2]x₁
POL(ISPALLISTKIND(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(TOP(x₁)) = 0
POL(U11'(x₁, x₂)) = 0
POL(U12'(x₁, x₂)) = 0
POL(U13'(x₁)) = x₁
POL(U21'(x₁, x₂, x₃)) = 0
POL(U22'(x₁, x₂, x₃)) = 0
POL(U23'(x₁, x₂, x₃)) = 0
POL(U24'(x₁, x₂, x₃)) = [2]x₁ + [2]x₃
POL(U25'(x₁, x₂)) = 0
POL(U26'(x₁)) = 0
POL(U31'(x₁, x₂)) = 0
POL(U32'(x₁, x₂)) = x₂
POL(U33'(x₁)) = 0
POL(U41'(x₁, x₂, x₃)) = 0
POL(U42'(x₁, x₂, x₃)) = 0
POL(U43'(x₁, x₂, x₃)) = 0
POL(U44'(x₁, x₂, x₃)) = 0
POL(U45'(x₁, x₂)) = 0
POL(U46'(x₁)) = 0
POL(U51'(x₁, x₂, x₃)) = 0
POL(U52'(x₁, x₂, x₃)) = [2]x₁
POL(U53'(x₁, x₂, x₃)) = 0
POL(U54'(x₁, x₂, x₃)) = [2]x₂
POL(U55'(x₁, x₂)) = [2]x₂
POL(U56'(x₁)) = 0
POL(U61'(x₁, x₂)) = 0
POL(U62'(x₁, x₂)) = 0
POL(U63'(x₁)) = 0
POL(U71'(x₁, x₂, x₃)) = 0
POL(U72'(x₁, x₂)) = [2]x₁
POL(U73'(x₁, x₂)) = 0
POL(U74'(x₁)) = 0
POL(U81'(x₁, x₂)) = 0
POL(U82'(x₁, x₂)) = 0
POL(U83'(x₁)) = [2]x₁
POL(U91'(x₁, x₂)) = 0
POL(U92'(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(a) = 0
POL(c(x₁)) = x₁
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c11(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c13(x₁)) = x₁
POL(c14(x₁)) = x₁
POL(c15(x₁)) = x₁
POL(c16(x₁)) = x₁
POL(c17(x₁)) = x₁
POL(c18(x₁)) = x₁
POL(c19(x₁)) = x₁
POL(c20(x₁)) = x₁
POL(c21(x₁)) = x₁
POL(c22(x₁)) = x₁
POL(c3(x₁)) = x₁
POL(c30(x₁)) = x₁
POL(c31(x₁)) = x₁
POL(c32(x₁)) = x₁
POL(c33(x₁)) = x₁
POL(c34(x₁)) = x₁
POL(c35(x₁)) = x₁
POL(c36(x₁)) = x₁
POL(c37(x₁)) = x₁
POL(c38(x₁)) = x₁
POL(c39(x₁)) = x₁
POL(c4(x₁)) = x₁
POL(c40(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(c46(x₁)) = x₁
POL(c47(x₁)) = x₁
POL(c48(x₁)) = x₁
POL(c49(x₁)) = x₁
POL(c5(x₁)) = x₁
POL(c50(x₁)) = x₁
POL(c51(x₁)) = x₁
POL(c52(x₁)) = x₁
POL(c53(x₁)) = x₁
POL(c54(x₁)) = x₁
POL(c55(x₁)) = x₁
POL(c56(x₁)) = x₁
POL(c57(x₁)) = x₁
POL(c58(x₁)) = x₁
POL(c59(x₁)) = x₁
POL(c6(x₁)) = x₁
POL(c60(x₁)) = x₁
POL(c61(x₁)) = x₁
POL(c62(x₁)) = x₁
POL(c63(x₁)) = x₁
POL(c64(x₁)) = x₁
POL(c65(x₁)) = x₁
POL(c66(x₁)) = x₁
POL(c67(x₁)) = x₁
POL(c68(x₁)) = x₁
POL(c69(x₁)) = x₁
POL(c7(x₁)) = x₁
POL(c70(x₁)) = x₁
POL(c71(x₁)) = x₁
POL(c72(x₁)) = x₁
POL(c73(x₁)) = x₁
POL(c74(x₁)) = x₁
POL(c75(x₁)) = x₁
POL(c76(x₁)) = x₁
POL(c77(x₁)) = x₁
POL(c78(x₁)) = x₁
POL(c79(x₁)) = x₁
POL(c8(x₁)) = x₁
POL(c80(x₁)) = x₁
POL(c81(x₁)) = x₁
POL(c82(x₁)) = x₁
POL(c83(x₁)) = x₁
POL(c84(x₁)) = x₁
POL(c85(x₁)) = x₁
POL(c86(x₁)) = x₁
POL(c87(x₁)) = x₁
POL(c88(x₁)) = x₁
POL(c89(x₁)) = x₁
POL(c9(x₁)) = x₁
POL(e) = 0
POL(i) = 0
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 0
POL(ok(x₁)) = [1] + x₁
POL(proper(x₁)) = 0
POL(tt) = 0
POL(u) = 0

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

proper(i) → ok(i)
proper(u) → ok(u)
proper(nil) → ok(nil)
proper(tt) → ok(tt)
proper(o) → ok(o)
proper(e) → ok(e)
proper(a) → ok(a)

Tuples:

U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U26'(ok(z0)) → c11(U26'(z0))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U33'(mark(z0)) → c19(U33'(z0))
U33'(ok(z0)) → c20(U33'(z0))
U92'(mark(z0)) → c21(U92'(z0))
U92'(ok(z0)) → c22(U92'(z0))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
__'(z0, mark(z1)) → c34(__'(z0, z1))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U83'(mark(z0)) → c43(U83'(z0))
U83'(ok(z0)) → c44(U83'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U13'(mark(z0)) → c54(U13'(z0))
U13'(ok(z0)) → c55(U13'(z0))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U56'(mark(z0)) → c58(U56'(z0))
U56'(ok(z0)) → c59(U56'(z0))
U46'(ok(z0)) → c60(U46'(z0))
U46'(mark(z0)) → c61(U46'(z0))
U74'(mark(z0)) → c62(U74'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
TOP(mark(z0)) → c3(TOP(proper(z0)))

S tuples:none
K tuples:

TOP(mark(z0)) → c3(TOP(proper(z0)))
U91'(ok(z0), ok(z1)) → c8(U91'(z0, z1))
U82'(ok(z0), ok(z1)) → c14(U82'(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c31(U52'(z0, z1, z2))
__'(mark(z0), z1) → c35(__'(z0, z1))
__'(ok(z0), ok(z1)) → c36(__'(z0, z1))
U73'(ok(z0), ok(z1)) → c37(U73'(z0, z1))
U73'(mark(z0), z1) → c38(U73'(z0, z1))
U63'(mark(z0)) → c39(U63'(z0))
U63'(ok(z0)) → c40(U63'(z0))
U62'(mark(z0), z1) → c41(U62'(z0, z1))
U62'(ok(z0), ok(z1)) → c42(U62'(z0, z1))
U53'(ok(z0), ok(z1), ok(z2)) → c64(U53'(z0, z1, z2))
U53'(mark(z0), z1, z2) → c65(U53'(z0, z1, z2))
U21'(ok(z0), ok(z1), ok(z2)) → c66(U21'(z0, z1, z2))
U24'(ok(z0), ok(z1), ok(z2)) → c70(U24'(z0, z1, z2))
U24'(mark(z0), z1, z2) → c71(U24'(z0, z1, z2))
ISQID(ok(z0)) → c72(ISQID(z0))
U44'(ok(z0), ok(z1), ok(z2)) → c79(U44'(z0, z1, z2))
ISLIST(ok(z0)) → c80(ISLIST(z0))
U25'(mark(z0), z1) → c68(U25'(z0, z1))
U44'(mark(z0), z1, z2) → c78(U44'(z0, z1, z2))
U32'(mark(z0), z1) → c5(U32'(z0, z1))
U21'(mark(z0), z1, z2) → c67(U21'(z0, z1, z2))
U81'(mark(z0), z1) → c82(U81'(z0, z1))
U45'(mark(z0), z1) → c51(U45'(z0, z1))
U11'(ok(z0), ok(z1)) → c(U11'(z0, z1))
ISNELIST(ok(z0)) → c4(ISNELIST(z0))
U43'(ok(z0), ok(z1), ok(z2)) → c9(U43'(z0, z1, z2))
U55'(ok(z0), ok(z1)) → c49(U55'(z0, z1))
U45'(ok(z0), ok(z1)) → c52(U45'(z0, z1))
U31'(ok(z0), ok(z1)) → c56(U31'(z0, z1))
U25'(ok(z0), ok(z1)) → c69(U25'(z0, z1))
U72'(ok(z0), ok(z1)) → c74(U72'(z0, z1))
ISPALLISTKIND(ok(z0)) → c83(ISPALLISTKIND(z0))
U12'(ok(z0), ok(z1)) → c86(U12'(z0, z1))
U43'(mark(z0), z1, z2) → c10(U43'(z0, z1, z2))
U23'(mark(z0), z1, z2) → c46(U23'(z0, z1, z2))
U11'(mark(z0), z1) → c1(U11'(z0, z1))
U22'(mark(z0), z1, z2) → c18(U22'(z0, z1, z2))
U55'(mark(z0), z1) → c50(U55'(z0, z1))
U31'(mark(z0), z1) → c57(U31'(z0, z1))
U72'(mark(z0), z1) → c73(U72'(z0, z1))
U26'(mark(z0)) → c12(U26'(z0))
U82'(mark(z0), z1) → c13(U82'(z0, z1))
U33'(mark(z0)) → c19(U33'(z0))
U83'(mark(z0)) → c43(U83'(z0))
U13'(mark(z0)) → c54(U13'(z0))
U12'(mark(z0), z1) → c87(U12'(z0, z1))
U61'(mark(z0), z1) → c16(U61'(z0, z1))
U46'(mark(z0)) → c61(U46'(z0))
U51'(mark(z0), z1, z2) → c32(U51'(z0, z1, z2))
U74'(mark(z0)) → c62(U74'(z0))
__'(z0, mark(z1)) → c34(__'(z0, z1))
U71'(mark(z0), z1, z2) → c77(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c33(U51'(z0, z1, z2))
U42'(ok(z0), ok(z1), ok(z2)) → c48(U42'(z0, z1, z2))
U61'(ok(z0), ok(z1)) → c15(U61'(z0, z1))
U22'(ok(z0), ok(z1), ok(z2)) → c17(U22'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c30(U52'(z0, z1, z2))
U91'(mark(z0), z1) → c7(U91'(z0, z1))
U92'(mark(z0)) → c21(U92'(z0))
U41'(mark(z0), z1, z2) → c88(U41'(z0, z1, z2))
U56'(mark(z0)) → c58(U56'(z0))
U81'(ok(z0), ok(z1)) → c81(U81'(z0, z1))
U26'(ok(z0)) → c11(U26'(z0))
U23'(ok(z0), ok(z1), ok(z2)) → c45(U23'(z0, z1, z2))
U46'(ok(z0)) → c60(U46'(z0))
U54'(ok(z0), ok(z1), ok(z2)) → c85(U54'(z0, z1, z2))
U42'(mark(z0), z1, z2) → c47(U42'(z0, z1, z2))
U54'(mark(z0), z1, z2) → c84(U54'(z0, z1, z2))
U56'(ok(z0)) → c59(U56'(z0))
U74'(ok(z0)) → c63(U74'(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c76(U71'(z0, z1, z2))
ISNEPAL(ok(z0)) → c75(ISNEPAL(z0))
U41'(ok(z0), ok(z1), ok(z2)) → c89(U41'(z0, z1, z2))
U83'(ok(z0)) → c44(U83'(z0))
U32'(ok(z0), ok(z1)) → c6(U32'(z0, z1))
U33'(ok(z0)) → c20(U33'(z0))
ISPAL(ok(z0)) → c53(ISPAL(z0))
U92'(ok(z0)) → c22(U92'(z0))
U13'(ok(z0)) → c55(U13'(z0))

Defined Rule Symbols:

proper

Defined Pair Symbols:

U11', ISNELIST, U32', U91', U43', U26', U82', U61', U22', U33', U92', U52', U51', __', U73', U63', U62', U83', U23', U42', U55', U45', ISPAL, U13', U31', U56', U46', U74', U53', U21', U25', U24', ISQID, U72', ISNEPAL, U71', U44', ISLIST, U81', ISPALLISTKIND, U54', U12', U41', TOP

Compound Symbols:

c, c1, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c3

(85) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)

The set S is empty