Runtime Complexity (innermost) proof of /tmp/tmp6hWu4I/PALINDROME_nokinds

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

0 CpxTRS

↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID), 0 ms)

↳2 CdtProblem

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

↳4 CdtProblem

↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

↳6 CdtProblem

↳7 CdtUsableRulesProof (⇔, 72 ms)

↳8 CdtProblem

↳9 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 1663 ms)

↳10 CdtProblem

↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 37 ms)

↳12 CdtProblem

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

↳14 CdtProblem

↳15 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

↳16 CdtProblem

↳17 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳18 CdtProblem

↳19 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 5 ms)

↳20 CdtProblem

↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳22 CdtProblem

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

↳24 CdtProblem

↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳26 CdtProblem

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

↳28 CdtProblem

↳29 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳30 CdtProblem

↳31 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID), 5 ms)

↳32 CdtProblem

↳33 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 4 ms)

↳34 CdtProblem

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

↳36 CdtProblem

↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳38 CdtProblem

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

↳40 CdtProblem

↳41 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 2 ms)

↳42 CdtProblem

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

↳44 CdtProblem

↳45 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 0 ms)

↳46 CdtProblem

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

↳48 CdtProblem

↳49 CdtNarrowingProof (BOTH BOUNDS(ID, ID), 38 ms)

↳50 CdtProblem

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

↳52 CdtProblem

↳53 CdtUnreachableProof (⇔, 0 ms)

↳54 CdtProblem

↳55 CdtUsableRulesProof (⇔, 0 ms)

↳56 CdtProblem

↳57 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳58 CdtProblem

↳59 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳60 CdtProblem

↳61 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 6 ms)

↳62 CdtProblem

↳63 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳64 CdtProblem

↳65 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳66 CdtProblem

↳67 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳68 CdtProblem

↳69 CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))), 0 ms)

↳70 CdtProblem

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

↳72 BOUNDS(O(1), O(1))

(0) Obligation:

Runtime Complexity TRS:
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(and(tt, X)) → mark(X)
active(isList(V)) → mark(isNeList(V))
active(isList(nil)) → mark(tt)
active(isList(__(V1, V2))) → mark(and(isList(V1), isList(V2)))
active(isNeList(V)) → mark(isQid(V))
active(isNeList(__(V1, V2))) → mark(and(isList(V1), isNeList(V2)))
active(isNeList(__(V1, V2))) → mark(and(isNeList(V1), isList(V2)))
active(isNePal(V)) → mark(isQid(V))
active(isNePal(__(I, __(P, I)))) → mark(and(isQid(I), isPal(P)))
active(isPal(V)) → mark(isNePal(V))
active(isPal(nil)) → mark(tt)
active(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(and(X1, X2)) → and(active(X1), X2)
__(mark(X1), X2) → mark(__(X1, X2))
__(X1, mark(X2)) → mark(__(X1, X2))
and(mark(X1), X2) → mark(and(X1, X2))
proper(__(X1, X2)) → __(proper(X1), proper(X2))
proper(nil) → ok(nil)
proper(and(X1, X2)) → and(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(isList(X)) → isList(proper(X))
proper(isNeList(X)) → isNeList(proper(X))
proper(isQid(X)) → isQid(proper(X))
proper(isNePal(X)) → isNePal(proper(X))
proper(isPal(X)) → isPal(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))
and(ok(X1), ok(X2)) → ok(and(X1, X2))
isList(ok(X)) → ok(isList(X))
isNeList(ok(X)) → ok(isNeList(X))
isQid(ok(X)) → ok(isQid(X))
isNePal(ok(X)) → ok(isNePal(X))
isPal(ok(X)) → ok(isPal(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST

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

Converted Cpx (relative) TRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(mark(z0), z1) → mark(__(z0, z1))
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isNePal(ok(z0)) → ok(isNePal(z0))
isPal(ok(z0)) → ok(isPal(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1
ACTIVE(__(nil, z0)) → c2
ACTIVE(and(tt, z0)) → c3
ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isList(nil)) → c5
ACTIVE(isList(__(z0, z1))) → c6(AND(isList(z0), isList(z1)), ISLIST(z0), ISLIST(z1))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c8(AND(isList(z0), isNeList(z1)), ISLIST(z0), ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c9(AND(isNeList(z0), isList(z1)), ISNELIST(z0), ISLIST(z1))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c11(AND(isQid(z0), isPal(z1)), ISQID(z0), ISPAL(z1))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(isPal(nil)) → c13
ACTIVE(isQid(a)) → c14
ACTIVE(isQid(e)) → c15
ACTIVE(isQid(i)) → c16
ACTIVE(isQid(o)) → c17
ACTIVE(isQid(u)) → c18
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(nil) → c28
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(tt) → c30
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
PROPER(a) → c36
PROPER(e) → c37
PROPER(i) → c38
PROPER(o) → c39
PROPER(u) → c40
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(__(z0, nil)) → c1
ACTIVE(__(nil, z0)) → c2
ACTIVE(and(tt, z0)) → c3
ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isList(nil)) → c5
ACTIVE(isList(__(z0, z1))) → c6(AND(isList(z0), isList(z1)), ISLIST(z0), ISLIST(z1))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c8(AND(isList(z0), isNeList(z1)), ISLIST(z0), ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c9(AND(isNeList(z0), isList(z1)), ISNELIST(z0), ISLIST(z1))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c11(AND(isQid(z0), isPal(z1)), ISQID(z0), ISPAL(z1))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(isPal(nil)) → c13
ACTIVE(isQid(a)) → c14
ACTIVE(isQid(e)) → c15
ACTIVE(isQid(i)) → c16
ACTIVE(isQid(o)) → c17
ACTIVE(isQid(u)) → c18
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(nil) → c28
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(tt) → c30
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
PROPER(a) → c36
PROPER(e) → c37
PROPER(i) → c38
PROPER(o) → c39
PROPER(u) → c40
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, __, and, proper, isList, isNeList, isQid, isNePal, isPal, top

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

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

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

Removed 17 trailing nodes:

ACTIVE(isQid(o)) → c17
PROPER(nil) → c28
ACTIVE(isQid(e)) → c15
ACTIVE(isList(nil)) → c5
PROPER(tt) → c30
ACTIVE(isPal(nil)) → c13
PROPER(e) → c37
PROPER(i) → c38
ACTIVE(isQid(a)) → c14
PROPER(o) → c39
ACTIVE(__(z0, nil)) → c1
PROPER(u) → c40
PROPER(a) → c36
ACTIVE(isQid(u)) → c18
ACTIVE(__(nil, z0)) → c2
ACTIVE(and(tt, z0)) → c3
ACTIVE(isQid(i)) → c16

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(mark(z0), z1) → mark(__(z0, z1))
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isNePal(ok(z0)) → ok(isNePal(z0))
isPal(ok(z0)) → ok(isPal(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isList(__(z0, z1))) → c6(AND(isList(z0), isList(z1)), ISLIST(z0), ISLIST(z1))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c8(AND(isList(z0), isNeList(z1)), ISLIST(z0), ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c9(AND(isNeList(z0), isList(z1)), ISNELIST(z0), ISLIST(z1))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c11(AND(isQid(z0), isPal(z1)), ISQID(z0), ISPAL(z1))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(__(__(z0, z1), z2)) → c(__'(z0, __(z1, z2)), __'(z1, z2))
ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isList(__(z0, z1))) → c6(AND(isList(z0), isList(z1)), ISLIST(z0), ISLIST(z1))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNeList(__(z0, z1))) → c8(AND(isList(z0), isNeList(z1)), ISLIST(z0), ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c9(AND(isNeList(z0), isList(z1)), ISNELIST(z0), ISLIST(z1))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c11(AND(isQid(z0), isPal(z1)), ISQID(z0), ISPAL(z1))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, __, and, proper, isList, isNeList, isQid, isNePal, isPal, top

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c, c4, c6, c7, c8, c9, c10, c11, c12, c19, c20, c21, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47

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

Split RHS of tuples not part of any SCC

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(mark(z0), z1) → mark(__(z0, z1))
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isNePal(ok(z0)) → ok(isNePal(z0))
isPal(ok(z0)) → ok(isPal(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

K tuples:none
Defined Rule Symbols:

active, __, and, proper, isList, isNeList, isQid, isNePal, isPal, top

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c21, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1

(7) CdtUsableRulesProof (EQUIVALENT transformation)

The following rules are not usable and were removed:

top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

K tuples:none
Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c21, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1

(9) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)

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

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

We considered the (Usable) Rules:

active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isQid(u)) → mark(tt)
active(isQid(a)) → mark(tt)
active(isPal(z0)) → mark(isNePal(z0))
active(and(z0, z1)) → and(active(z0), z1)
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
proper(e) → ok(e)
proper(isPal(z0)) → isPal(proper(z0))
active(__(nil, z0)) → mark(z0)
active(__(z0, nil)) → mark(z0)
__(z0, mark(z1)) → mark(__(z0, z1))
isNeList(ok(z0)) → ok(isNeList(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
active(isQid(o)) → mark(tt)
__(ok(z0), ok(z1)) → ok(__(z0, z1))
proper(isQid(z0)) → isQid(proper(z0))
proper(isList(z0)) → isList(proper(z0))
and(mark(z0), z1) → mark(and(z0, z1))
proper(nil) → ok(nil)
active(__(z0, z1)) → __(active(z0), z1)
proper(a) → ok(a)
proper(o) → ok(o)
active(isQid(i)) → mark(tt)
active(__(z0, z1)) → __(z0, active(z1))
proper(u) → ok(u)
active(isList(z0)) → mark(isNeList(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
isQid(ok(z0)) → ok(isQid(z0))
proper(and(z0, z1)) → and(proper(z0), proper(z1))
__(mark(z0), z1) → mark(__(z0, z1))
active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(and(tt, z0)) → mark(z0)
isPal(ok(z0)) → ok(isPal(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
active(isList(nil)) → mark(tt)
active(isNePal(z0)) → mark(isQid(z0))
isList(ok(z0)) → ok(isList(z0))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
active(isQid(e)) → mark(tt)
isNePal(ok(z0)) → ok(isNePal(z0))
proper(tt) → ok(tt)
active(isNeList(z0)) → mark(isQid(z0))
proper(i) → ok(i)
active(isPal(nil)) → mark(tt)

And the Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

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

POL(ACTIVE(x₁)) = 0
POL(AND(x₁, x₂)) = 0
POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(PROPER(x₁)) = 0
POL(TOP(x₁)) = x₁
POL(__(x₁, x₂)) = [1] + [4]x₁ + x₂
POL(__'(x₁, x₂)) = 0
POL(a) = [4]
POL(active(x₁)) = x₁
POL(and(x₁, x₂)) = x₁ + x₂
POL(c1(x₁)) = x₁
POL(c10(x₁)) = x₁
POL(c12(x₁)) = x₁
POL(c19(x₁, x₂)) = x₁ + x₂
POL(c20(x₁, x₂)) = x₁ + x₂
POL(c21(x₁, x₂)) = x₁ + x₂
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c27(x₁, x₂, x₃)) = x₁ + x₂ + x₃
POL(c29(x₁, x₂, x₃)) = x₁ + x₂ + x₃
POL(c31(x₁, x₂)) = x₁ + x₂
POL(c32(x₁, x₂)) = x₁ + x₂
POL(c33(x₁, x₂)) = x₁ + x₂
POL(c34(x₁, x₂)) = x₁ + x₂
POL(c35(x₁, x₂)) = x₁ + x₂
POL(c4(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, x₂)) = x₁ + x₂
POL(c47(x₁, x₂)) = x₁ + x₂
POL(c7(x₁)) = x₁
POL(e) = [4]
POL(i) = [4]
POL(isList(x₁)) = [3] + [4]x₁
POL(isNeList(x₁)) = [1] + [4]x₁
POL(isNePal(x₁)) = [4] + [4]x₁
POL(isPal(x₁)) = [5] + [4]x₁
POL(isQid(x₁)) = [4]x₁
POL(mark(x₁)) = [1] + x₁
POL(nil) = 0
POL(o) = [4]
POL(ok(x₁)) = x₁
POL(proper(x₁)) = x₁
POL(tt) = [1]
POL(u) = [1]

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c21, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1

(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(and(z0, z1)) → c21(AND(active(z0), z1), ACTIVE(z0)) by

ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(and(tt, z0)))
ACTIVE(and(isList(z0), x1)) → c21(AND(mark(isNeList(z0)), x1), ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isList(z1))), x1), ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isNeList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isNeList(z0), isList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNePal(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c21(AND(mark(and(isQid(z0), isPal(z1))), x1), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c21(AND(mark(isNePal(z0)), x1), ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isPal(nil)))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(a)))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(e)))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(i)))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(o)))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(u)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(and(tt, z0)))
ACTIVE(and(isList(z0), x1)) → c21(AND(mark(isNeList(z0)), x1), ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isList(z1))), x1), ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isNeList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isNeList(z0), isList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNePal(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c21(AND(mark(and(isQid(z0), isPal(z1))), x1), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c21(AND(mark(isNePal(z0)), x1), ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isPal(nil)))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(a)))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(e)))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(i)))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(o)))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(u)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(and(tt, z0)))
ACTIVE(and(isList(z0), x1)) → c21(AND(mark(isNeList(z0)), x1), ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isList(z1))), x1), ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isNeList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isNeList(z0), isList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNePal(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c21(AND(mark(and(isQid(z0), isPal(z1))), x1), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c21(AND(mark(isNePal(z0)), x1), ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isPal(nil)))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(a)))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(e)))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(i)))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(o)))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1), ACTIVE(isQid(u)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21

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

Removed 6 trailing tuple parts

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(isList(z0), x1)) → c21(AND(mark(isNeList(z0)), x1), ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isList(z1))), x1), ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isNeList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isNeList(z0), isList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNePal(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c21(AND(mark(and(isQid(z0), isPal(z1))), x1), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c21(AND(mark(isNePal(z0)), x1), ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isPal(nil)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(isList(z0), x1)) → c21(AND(mark(isNeList(z0)), x1), ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isList(z1))), x1), ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isList(z0), isNeList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c21(AND(mark(and(isNeList(z0), isList(z1))), x1), ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNePal(z0), x1)) → c21(AND(mark(isQid(z0)), x1), ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c21(AND(mark(and(isQid(z0), isPal(z1))), x1), ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c21(AND(mark(isNePal(z0)), x1), ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c21(AND(mark(tt), x1), ACTIVE(isPal(nil)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21

(15) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c27, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c

(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(__(z0, z1)) → c27(__'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0), PROPER(a))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0), PROPER(e))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0), PROPER(i))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0), PROPER(o))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0), PROPER(u))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(a), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(e), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(i), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(o), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(u), PROPER(x1))

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0), PROPER(a))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0), PROPER(e))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0), PROPER(i))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0), PROPER(o))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0), PROPER(u))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(a), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(e), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(i), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(o), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(u), PROPER(x1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0), PROPER(a))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0), PROPER(e))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0), PROPER(i))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0), PROPER(o))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0), PROPER(u))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(a), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(e), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(i), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(o), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(u), PROPER(x1))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27

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

Removed 14 trailing tuple parts

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c29, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(and(z0, z1)) → c29(AND(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0), PROPER(a))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0), PROPER(e))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0), PROPER(i))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0), PROPER(o))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0), PROPER(u))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(a), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(e), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(i), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(o), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(u), PROPER(x1))

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0), PROPER(a))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0), PROPER(e))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0), PROPER(i))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0), PROPER(o))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0), PROPER(u))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(a), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(e), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(i), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(o), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(u), PROPER(x1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0), PROPER(nil))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0), PROPER(a))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0), PROPER(e))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0), PROPER(i))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0), PROPER(o))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0), PROPER(u))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(a), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(e), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(i), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(o), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(u), PROPER(x1))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29

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

Removed 14 trailing tuple parts

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c31, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29

(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(isList(z0)) → c31(ISLIST(proper(z0)), PROPER(z0)) by

PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)), PROPER(nil))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)), PROPER(tt))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(a)) → c31(ISLIST(ok(a)), PROPER(a))
PROPER(isList(e)) → c31(ISLIST(ok(e)), PROPER(e))
PROPER(isList(i)) → c31(ISLIST(ok(i)), PROPER(i))
PROPER(isList(o)) → c31(ISLIST(ok(o)), PROPER(o))
PROPER(isList(u)) → c31(ISLIST(ok(u)), PROPER(u))

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)), PROPER(nil))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)), PROPER(tt))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(a)) → c31(ISLIST(ok(a)), PROPER(a))
PROPER(isList(e)) → c31(ISLIST(ok(e)), PROPER(e))
PROPER(isList(i)) → c31(ISLIST(ok(i)), PROPER(i))
PROPER(isList(o)) → c31(ISLIST(ok(o)), PROPER(o))
PROPER(isList(u)) → c31(ISLIST(ok(u)), PROPER(u))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)), PROPER(nil))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)), PROPER(tt))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(a)) → c31(ISLIST(ok(a)), PROPER(a))
PROPER(isList(e)) → c31(ISLIST(ok(e)), PROPER(e))
PROPER(isList(i)) → c31(ISLIST(ok(i)), PROPER(i))
PROPER(isList(o)) → c31(ISLIST(ok(o)), PROPER(o))
PROPER(isList(u)) → c31(ISLIST(ok(u)), PROPER(u))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31

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

Removed 7 trailing tuple parts

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c32, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31

(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(isNeList(z0)) → c32(ISNELIST(proper(z0)), PROPER(z0)) by

PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)), PROPER(nil))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)), PROPER(tt))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)), PROPER(a))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)), PROPER(e))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)), PROPER(i))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)), PROPER(o))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)), PROPER(u))

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)), PROPER(nil))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)), PROPER(tt))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)), PROPER(a))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)), PROPER(e))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)), PROPER(i))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)), PROPER(o))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)), PROPER(u))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)), PROPER(nil))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)), PROPER(tt))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)), PROPER(a))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)), PROPER(e))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)), PROPER(i))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)), PROPER(o))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)), PROPER(u))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32

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

Removed 7 trailing tuple parts

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c33, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(isQid(z0)) → c33(ISQID(proper(z0)), PROPER(z0)) by

PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)), PROPER(nil))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)), PROPER(tt))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(a)) → c33(ISQID(ok(a)), PROPER(a))
PROPER(isQid(e)) → c33(ISQID(ok(e)), PROPER(e))
PROPER(isQid(i)) → c33(ISQID(ok(i)), PROPER(i))
PROPER(isQid(o)) → c33(ISQID(ok(o)), PROPER(o))
PROPER(isQid(u)) → c33(ISQID(ok(u)), PROPER(u))

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)), PROPER(nil))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)), PROPER(tt))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(a)) → c33(ISQID(ok(a)), PROPER(a))
PROPER(isQid(e)) → c33(ISQID(ok(e)), PROPER(e))
PROPER(isQid(i)) → c33(ISQID(ok(i)), PROPER(i))
PROPER(isQid(o)) → c33(ISQID(ok(o)), PROPER(o))
PROPER(isQid(u)) → c33(ISQID(ok(u)), PROPER(u))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)), PROPER(nil))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)), PROPER(tt))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(a)) → c33(ISQID(ok(a)), PROPER(a))
PROPER(isQid(e)) → c33(ISQID(ok(e)), PROPER(e))
PROPER(isQid(i)) → c33(ISQID(ok(i)), PROPER(i))
PROPER(isQid(o)) → c33(ISQID(ok(o)), PROPER(o))
PROPER(isQid(u)) → c33(ISQID(ok(u)), PROPER(u))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33

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

Removed 7 trailing tuple parts

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c34, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33

(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(isNePal(z0)) → c34(ISNEPAL(proper(z0)), PROPER(z0)) by

PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)), PROPER(a))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)), PROPER(e))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)), PROPER(i))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)), PROPER(o))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)), PROPER(u))

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)), PROPER(a))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)), PROPER(e))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)), PROPER(i))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)), PROPER(o))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)), PROPER(u))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)), PROPER(nil))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)), PROPER(tt))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)), PROPER(a))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)), PROPER(e))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)), PROPER(i))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)), PROPER(o))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)), PROPER(u))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34

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

Removed 7 trailing tuple parts

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, PROPER, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c35, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34

(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(isPal(z0)) → c35(ISPAL(proper(z0)), PROPER(z0)) by

PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)), PROPER(nil))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)), PROPER(tt))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)), PROPER(a))
PROPER(isPal(e)) → c35(ISPAL(ok(e)), PROPER(e))
PROPER(isPal(i)) → c35(ISPAL(ok(i)), PROPER(i))
PROPER(isPal(o)) → c35(ISPAL(ok(o)), PROPER(o))
PROPER(isPal(u)) → c35(ISPAL(ok(u)), PROPER(u))

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)), PROPER(nil))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)), PROPER(tt))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)), PROPER(a))
PROPER(isPal(e)) → c35(ISPAL(ok(e)), PROPER(e))
PROPER(isPal(i)) → c35(ISPAL(ok(i)), PROPER(i))
PROPER(isPal(o)) → c35(ISPAL(ok(o)), PROPER(o))
PROPER(isPal(u)) → c35(ISPAL(ok(u)), PROPER(u))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)), PROPER(nil))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)), PROPER(tt))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)), PROPER(a))
PROPER(isPal(e)) → c35(ISPAL(ok(e)), PROPER(e))
PROPER(isPal(i)) → c35(ISPAL(ok(i)), PROPER(i))
PROPER(isPal(o)) → c35(ISPAL(ok(o)), PROPER(o))
PROPER(isPal(u)) → c35(ISPAL(ok(u)), PROPER(u))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP, PROPER

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35

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

Removed 7 trailing tuple parts

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP, PROPER

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c41, c42, c43, c44, c45, c46, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(__(z0, z1))) → c46(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
TOP(mark(nil)) → c46(TOP(ok(nil)), PROPER(nil))
TOP(mark(and(z0, z1))) → c46(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
TOP(mark(tt)) → c46(TOP(ok(tt)), PROPER(tt))
TOP(mark(isList(z0))) → c46(TOP(isList(proper(z0))), PROPER(isList(z0)))
TOP(mark(isNeList(z0))) → c46(TOP(isNeList(proper(z0))), PROPER(isNeList(z0)))
TOP(mark(isQid(z0))) → c46(TOP(isQid(proper(z0))), PROPER(isQid(z0)))
TOP(mark(isNePal(z0))) → c46(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
TOP(mark(isPal(z0))) → c46(TOP(isPal(proper(z0))), PROPER(isPal(z0)))
TOP(mark(a)) → c46(TOP(ok(a)), PROPER(a))
TOP(mark(e)) → c46(TOP(ok(e)), PROPER(e))
TOP(mark(i)) → c46(TOP(ok(i)), PROPER(i))
TOP(mark(o)) → c46(TOP(ok(o)), PROPER(o))
TOP(mark(u)) → c46(TOP(ok(u)), PROPER(u))

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(mark(__(z0, z1))) → c46(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
TOP(mark(nil)) → c46(TOP(ok(nil)), PROPER(nil))
TOP(mark(and(z0, z1))) → c46(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
TOP(mark(tt)) → c46(TOP(ok(tt)), PROPER(tt))
TOP(mark(isList(z0))) → c46(TOP(isList(proper(z0))), PROPER(isList(z0)))
TOP(mark(isNeList(z0))) → c46(TOP(isNeList(proper(z0))), PROPER(isNeList(z0)))
TOP(mark(isQid(z0))) → c46(TOP(isQid(proper(z0))), PROPER(isQid(z0)))
TOP(mark(isNePal(z0))) → c46(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
TOP(mark(isPal(z0))) → c46(TOP(isPal(proper(z0))), PROPER(isPal(z0)))
TOP(mark(a)) → c46(TOP(ok(a)), PROPER(a))
TOP(mark(e)) → c46(TOP(ok(e)), PROPER(e))
TOP(mark(i)) → c46(TOP(ok(i)), PROPER(i))
TOP(mark(o)) → c46(TOP(ok(o)), PROPER(o))
TOP(mark(u)) → c46(TOP(ok(u)), PROPER(u))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP, PROPER

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c41, c42, c43, c44, c45, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c46

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

Removed 7 trailing tuple parts

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(mark(__(z0, z1))) → c46(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
TOP(mark(and(z0, z1))) → c46(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
TOP(mark(isList(z0))) → c46(TOP(isList(proper(z0))), PROPER(isList(z0)))
TOP(mark(isNeList(z0))) → c46(TOP(isNeList(proper(z0))), PROPER(isNeList(z0)))
TOP(mark(isQid(z0))) → c46(TOP(isQid(proper(z0))), PROPER(isQid(z0)))
TOP(mark(isNePal(z0))) → c46(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
TOP(mark(isPal(z0))) → c46(TOP(isPal(proper(z0))), PROPER(isPal(z0)))
TOP(mark(nil)) → c46(TOP(ok(nil)))
TOP(mark(tt)) → c46(TOP(ok(tt)))
TOP(mark(a)) → c46(TOP(ok(a)))
TOP(mark(e)) → c46(TOP(ok(e)))
TOP(mark(i)) → c46(TOP(ok(i)))
TOP(mark(o)) → c46(TOP(ok(o)))
TOP(mark(u)) → c46(TOP(ok(u)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, TOP, PROPER

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c41, c42, c43, c44, c45, c47, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c46, c46

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(ok(z0)) → c47(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(__(__(z0, z1), z2))) → c47(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
TOP(ok(__(z0, nil))) → c47(TOP(mark(z0)), ACTIVE(__(z0, nil)))
TOP(ok(__(nil, z0))) → c47(TOP(mark(z0)), ACTIVE(__(nil, z0)))
TOP(ok(and(tt, z0))) → c47(TOP(mark(z0)), ACTIVE(and(tt, z0)))
TOP(ok(isList(z0))) → c47(TOP(mark(isNeList(z0))), ACTIVE(isList(z0)))
TOP(ok(isList(nil))) → c47(TOP(mark(tt)), ACTIVE(isList(nil)))
TOP(ok(isList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isList(z1)))), ACTIVE(isList(__(z0, z1))))
TOP(ok(isNeList(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNeList(z0)))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isNeList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isNeList(z0), isList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNePal(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNePal(z0)))
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c47(TOP(mark(and(isQid(z0), isPal(z1)))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
TOP(ok(isPal(z0))) → c47(TOP(mark(isNePal(z0))), ACTIVE(isPal(z0)))
TOP(ok(isPal(nil))) → c47(TOP(mark(tt)), ACTIVE(isPal(nil)))
TOP(ok(isQid(a))) → c47(TOP(mark(tt)), ACTIVE(isQid(a)))
TOP(ok(isQid(e))) → c47(TOP(mark(tt)), ACTIVE(isQid(e)))
TOP(ok(isQid(i))) → c47(TOP(mark(tt)), ACTIVE(isQid(i)))
TOP(ok(isQid(o))) → c47(TOP(mark(tt)), ACTIVE(isQid(o)))
TOP(ok(isQid(u))) → c47(TOP(mark(tt)), ACTIVE(isQid(u)))
TOP(ok(__(z0, z1))) → c47(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1)))
TOP(ok(__(z0, z1))) → c47(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1)))
TOP(ok(and(z0, z1))) → c47(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(mark(__(z0, z1))) → c46(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
TOP(mark(and(z0, z1))) → c46(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
TOP(mark(isList(z0))) → c46(TOP(isList(proper(z0))), PROPER(isList(z0)))
TOP(mark(isNeList(z0))) → c46(TOP(isNeList(proper(z0))), PROPER(isNeList(z0)))
TOP(mark(isQid(z0))) → c46(TOP(isQid(proper(z0))), PROPER(isQid(z0)))
TOP(mark(isNePal(z0))) → c46(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
TOP(mark(isPal(z0))) → c46(TOP(isPal(proper(z0))), PROPER(isPal(z0)))
TOP(mark(nil)) → c46(TOP(ok(nil)))
TOP(mark(tt)) → c46(TOP(ok(tt)))
TOP(mark(a)) → c46(TOP(ok(a)))
TOP(mark(e)) → c46(TOP(ok(e)))
TOP(mark(i)) → c46(TOP(ok(i)))
TOP(mark(o)) → c46(TOP(ok(o)))
TOP(mark(u)) → c46(TOP(ok(u)))
TOP(ok(__(__(z0, z1), z2))) → c47(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
TOP(ok(__(z0, nil))) → c47(TOP(mark(z0)), ACTIVE(__(z0, nil)))
TOP(ok(__(nil, z0))) → c47(TOP(mark(z0)), ACTIVE(__(nil, z0)))
TOP(ok(and(tt, z0))) → c47(TOP(mark(z0)), ACTIVE(and(tt, z0)))
TOP(ok(isList(z0))) → c47(TOP(mark(isNeList(z0))), ACTIVE(isList(z0)))
TOP(ok(isList(nil))) → c47(TOP(mark(tt)), ACTIVE(isList(nil)))
TOP(ok(isList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isList(z1)))), ACTIVE(isList(__(z0, z1))))
TOP(ok(isNeList(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNeList(z0)))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isNeList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isNeList(z0), isList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNePal(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNePal(z0)))
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c47(TOP(mark(and(isQid(z0), isPal(z1)))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
TOP(ok(isPal(z0))) → c47(TOP(mark(isNePal(z0))), ACTIVE(isPal(z0)))
TOP(ok(isPal(nil))) → c47(TOP(mark(tt)), ACTIVE(isPal(nil)))
TOP(ok(isQid(a))) → c47(TOP(mark(tt)), ACTIVE(isQid(a)))
TOP(ok(isQid(e))) → c47(TOP(mark(tt)), ACTIVE(isQid(e)))
TOP(ok(isQid(i))) → c47(TOP(mark(tt)), ACTIVE(isQid(i)))
TOP(ok(isQid(o))) → c47(TOP(mark(tt)), ACTIVE(isQid(o)))
TOP(ok(isQid(u))) → c47(TOP(mark(tt)), ACTIVE(isQid(u)))
TOP(ok(__(z0, z1))) → c47(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1)))
TOP(ok(__(z0, z1))) → c47(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1)))
TOP(ok(and(z0, z1))) → c47(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(ok(__(__(z0, z1), z2))) → c47(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
TOP(ok(__(z0, nil))) → c47(TOP(mark(z0)), ACTIVE(__(z0, nil)))
TOP(ok(__(nil, z0))) → c47(TOP(mark(z0)), ACTIVE(__(nil, z0)))
TOP(ok(and(tt, z0))) → c47(TOP(mark(z0)), ACTIVE(and(tt, z0)))
TOP(ok(isList(z0))) → c47(TOP(mark(isNeList(z0))), ACTIVE(isList(z0)))
TOP(ok(isList(nil))) → c47(TOP(mark(tt)), ACTIVE(isList(nil)))
TOP(ok(isList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isList(z1)))), ACTIVE(isList(__(z0, z1))))
TOP(ok(isNeList(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNeList(z0)))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isNeList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isNeList(z0), isList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNePal(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNePal(z0)))
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c47(TOP(mark(and(isQid(z0), isPal(z1)))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
TOP(ok(isPal(z0))) → c47(TOP(mark(isNePal(z0))), ACTIVE(isPal(z0)))
TOP(ok(isPal(nil))) → c47(TOP(mark(tt)), ACTIVE(isPal(nil)))
TOP(ok(isQid(a))) → c47(TOP(mark(tt)), ACTIVE(isQid(a)))
TOP(ok(isQid(e))) → c47(TOP(mark(tt)), ACTIVE(isQid(e)))
TOP(ok(isQid(i))) → c47(TOP(mark(tt)), ACTIVE(isQid(i)))
TOP(ok(isQid(o))) → c47(TOP(mark(tt)), ACTIVE(isQid(o)))
TOP(ok(isQid(u))) → c47(TOP(mark(tt)), ACTIVE(isQid(u)))
TOP(ok(__(z0, z1))) → c47(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1)))
TOP(ok(__(z0, z1))) → c47(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1)))
TOP(ok(and(z0, z1))) → c47(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))

K tuples:

TOP(mark(z0)) → c46(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, PROPER, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c41, c42, c43, c44, c45, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c46, c46, c47

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

Removed 7 trailing nodes:

TOP(mark(e)) → c46(TOP(ok(e)))
TOP(mark(tt)) → c46(TOP(ok(tt)))
TOP(mark(i)) → c46(TOP(ok(i)))
TOP(mark(nil)) → c46(TOP(ok(nil)))
TOP(mark(u)) → c46(TOP(ok(u)))
TOP(mark(a)) → c46(TOP(ok(a)))
TOP(mark(o)) → c46(TOP(ok(o)))

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(mark(__(z0, z1))) → c46(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
TOP(mark(and(z0, z1))) → c46(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
TOP(mark(isList(z0))) → c46(TOP(isList(proper(z0))), PROPER(isList(z0)))
TOP(mark(isNeList(z0))) → c46(TOP(isNeList(proper(z0))), PROPER(isNeList(z0)))
TOP(mark(isQid(z0))) → c46(TOP(isQid(proper(z0))), PROPER(isQid(z0)))
TOP(mark(isNePal(z0))) → c46(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
TOP(mark(isPal(z0))) → c46(TOP(isPal(proper(z0))), PROPER(isPal(z0)))
TOP(ok(__(__(z0, z1), z2))) → c47(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
TOP(ok(__(z0, nil))) → c47(TOP(mark(z0)), ACTIVE(__(z0, nil)))
TOP(ok(__(nil, z0))) → c47(TOP(mark(z0)), ACTIVE(__(nil, z0)))
TOP(ok(and(tt, z0))) → c47(TOP(mark(z0)), ACTIVE(and(tt, z0)))
TOP(ok(isList(z0))) → c47(TOP(mark(isNeList(z0))), ACTIVE(isList(z0)))
TOP(ok(isList(nil))) → c47(TOP(mark(tt)), ACTIVE(isList(nil)))
TOP(ok(isList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isList(z1)))), ACTIVE(isList(__(z0, z1))))
TOP(ok(isNeList(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNeList(z0)))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isNeList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isNeList(z0), isList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNePal(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNePal(z0)))
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c47(TOP(mark(and(isQid(z0), isPal(z1)))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
TOP(ok(isPal(z0))) → c47(TOP(mark(isNePal(z0))), ACTIVE(isPal(z0)))
TOP(ok(isPal(nil))) → c47(TOP(mark(tt)), ACTIVE(isPal(nil)))
TOP(ok(isQid(a))) → c47(TOP(mark(tt)), ACTIVE(isQid(a)))
TOP(ok(isQid(e))) → c47(TOP(mark(tt)), ACTIVE(isQid(e)))
TOP(ok(isQid(i))) → c47(TOP(mark(tt)), ACTIVE(isQid(i)))
TOP(ok(isQid(o))) → c47(TOP(mark(tt)), ACTIVE(isQid(o)))
TOP(ok(isQid(u))) → c47(TOP(mark(tt)), ACTIVE(isQid(u)))
TOP(ok(__(z0, z1))) → c47(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1)))
TOP(ok(__(z0, z1))) → c47(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1)))
TOP(ok(and(z0, z1))) → c47(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))

S tuples:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(ok(__(__(z0, z1), z2))) → c47(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
TOP(ok(__(z0, nil))) → c47(TOP(mark(z0)), ACTIVE(__(z0, nil)))
TOP(ok(__(nil, z0))) → c47(TOP(mark(z0)), ACTIVE(__(nil, z0)))
TOP(ok(and(tt, z0))) → c47(TOP(mark(z0)), ACTIVE(and(tt, z0)))
TOP(ok(isList(z0))) → c47(TOP(mark(isNeList(z0))), ACTIVE(isList(z0)))
TOP(ok(isList(nil))) → c47(TOP(mark(tt)), ACTIVE(isList(nil)))
TOP(ok(isList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isList(z1)))), ACTIVE(isList(__(z0, z1))))
TOP(ok(isNeList(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNeList(z0)))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isNeList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isNeList(z0), isList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNePal(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNePal(z0)))
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c47(TOP(mark(and(isQid(z0), isPal(z1)))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
TOP(ok(isPal(z0))) → c47(TOP(mark(isNePal(z0))), ACTIVE(isPal(z0)))
TOP(ok(isPal(nil))) → c47(TOP(mark(tt)), ACTIVE(isPal(nil)))
TOP(ok(isQid(a))) → c47(TOP(mark(tt)), ACTIVE(isQid(a)))
TOP(ok(isQid(e))) → c47(TOP(mark(tt)), ACTIVE(isQid(e)))
TOP(ok(isQid(i))) → c47(TOP(mark(tt)), ACTIVE(isQid(i)))
TOP(ok(isQid(o))) → c47(TOP(mark(tt)), ACTIVE(isQid(o)))
TOP(ok(isQid(u))) → c47(TOP(mark(tt)), ACTIVE(isQid(u)))
TOP(ok(__(z0, z1))) → c47(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1)))
TOP(ok(__(z0, z1))) → c47(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1)))
TOP(ok(and(z0, z1))) → c47(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

ACTIVE, __', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL, PROPER, TOP

Compound Symbols:

c4, c7, c10, c12, c19, c20, c22, c23, c24, c25, c26, c41, c42, c43, c44, c45, c1, c21, c21, c, c27, c27, c29, c29, c31, c31, c32, c32, c33, c33, c34, c34, c35, c35, c46, c47

(53) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(isList(z0)) → c4(ISNELIST(z0))
ACTIVE(isNeList(z0)) → c7(ISQID(z0))
ACTIVE(isNePal(z0)) → c10(ISQID(z0))
ACTIVE(isPal(z0)) → c12(ISNEPAL(z0))
ACTIVE(__(z0, z1)) → c19(__'(active(z0), z1), ACTIVE(z0))
ACTIVE(__(z0, z1)) → c20(__'(z0, active(z1)), ACTIVE(z1))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z0, __(z1, z2)))
ACTIVE(__(__(z0, z1), z2)) → c1(__'(z1, z2))
ACTIVE(isList(__(z0, z1))) → c1(AND(isList(z0), isList(z1)))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isList(z0), isNeList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z1))
ACTIVE(isNeList(__(z0, z1))) → c1(AND(isNeList(z0), isList(z1)))
ACTIVE(isNeList(__(z0, z1))) → c1(ISNELIST(z0))
ACTIVE(isNeList(__(z0, z1))) → c1(ISLIST(z1))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(AND(isQid(z0), isPal(z1)))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISQID(z0))
ACTIVE(isNePal(__(z0, __(z1, z0)))) → c1(ISPAL(z1))
ACTIVE(and(__(__(z0, z1), z2), x1)) → c21(AND(mark(__(z0, __(z1, z2))), x1), ACTIVE(__(__(z0, z1), z2)))
ACTIVE(and(__(z0, nil), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(z0, nil)))
ACTIVE(and(__(nil, z0), x1)) → c21(AND(mark(z0), x1), ACTIVE(__(nil, z0)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(active(z0), z1), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(__(z0, z1), x1)) → c21(AND(__(z0, active(z1)), x1), ACTIVE(__(z0, z1)))
ACTIVE(and(and(z0, z1), x1)) → c21(AND(and(active(z0), z1), x1), ACTIVE(and(z0, z1)))
ACTIVE(and(and(tt, z0), x1)) → c21(AND(mark(z0), x1))
ACTIVE(and(isQid(a), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(e), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(i), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(o), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isQid(u), x1)) → c21(AND(mark(tt), x1))
ACTIVE(and(isList(z0), x1)) → c(AND(mark(isNeList(z0)), x1))
ACTIVE(and(isList(z0), x1)) → c(ACTIVE(isList(z0)))
ACTIVE(and(isList(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isList(nil), x1)) → c(ACTIVE(isList(nil)))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isList(z1))), x1))
ACTIVE(and(isList(__(z0, z1)), x1)) → c(ACTIVE(isList(__(z0, z1))))
ACTIVE(and(isNeList(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNeList(z0), x1)) → c(ACTIVE(isNeList(z0)))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isList(z0), isNeList(z1))), x1))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(ACTIVE(isNeList(__(z0, z1))))
ACTIVE(and(isNeList(__(z0, z1)), x1)) → c(AND(mark(and(isNeList(z0), isList(z1))), x1))
ACTIVE(and(isNePal(z0), x1)) → c(AND(mark(isQid(z0)), x1))
ACTIVE(and(isNePal(z0), x1)) → c(ACTIVE(isNePal(z0)))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(AND(mark(and(isQid(z0), isPal(z1))), x1))
ACTIVE(and(isNePal(__(z0, __(z1, z0))), x1)) → c(ACTIVE(isNePal(__(z0, __(z1, z0)))))
ACTIVE(and(isPal(z0), x1)) → c(AND(mark(isNePal(z0)), x1))
ACTIVE(and(isPal(z0), x1)) → c(ACTIVE(isPal(z0)))
ACTIVE(and(isPal(nil), x1)) → c(AND(mark(tt), x1))
ACTIVE(and(isPal(nil), x1)) → c(ACTIVE(isPal(nil)))
PROPER(__(x0, __(z0, z1))) → c27(__'(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(__(x0, and(z0, z1))) → c27(__'(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(__(x0, isList(z0))) → c27(__'(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(__(x0, isNeList(z0))) → c27(__'(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(__(x0, isQid(z0))) → c27(__'(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(__(x0, isNePal(z0))) → c27(__'(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(__(x0, isPal(z0))) → c27(__'(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(__(__(z0, z1), x1)) → c27(__'(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(__(and(z0, z1), x1)) → c27(__'(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(__(isList(z0), x1)) → c27(__'(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(__(isNeList(z0), x1)) → c27(__'(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(__(isQid(z0), x1)) → c27(__'(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(__(isNePal(z0), x1)) → c27(__'(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(__(isPal(z0), x1)) → c27(__'(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(__(x0, nil)) → c27(__'(proper(x0), ok(nil)), PROPER(x0))
PROPER(__(x0, tt)) → c27(__'(proper(x0), ok(tt)), PROPER(x0))
PROPER(__(x0, a)) → c27(__'(proper(x0), ok(a)), PROPER(x0))
PROPER(__(x0, e)) → c27(__'(proper(x0), ok(e)), PROPER(x0))
PROPER(__(x0, i)) → c27(__'(proper(x0), ok(i)), PROPER(x0))
PROPER(__(x0, o)) → c27(__'(proper(x0), ok(o)), PROPER(x0))
PROPER(__(x0, u)) → c27(__'(proper(x0), ok(u)), PROPER(x0))
PROPER(__(nil, x1)) → c27(__'(ok(nil), proper(x1)), PROPER(x1))
PROPER(__(tt, x1)) → c27(__'(ok(tt), proper(x1)), PROPER(x1))
PROPER(__(a, x1)) → c27(__'(ok(a), proper(x1)), PROPER(x1))
PROPER(__(e, x1)) → c27(__'(ok(e), proper(x1)), PROPER(x1))
PROPER(__(i, x1)) → c27(__'(ok(i), proper(x1)), PROPER(x1))
PROPER(__(o, x1)) → c27(__'(ok(o), proper(x1)), PROPER(x1))
PROPER(__(u, x1)) → c27(__'(ok(u), proper(x1)), PROPER(x1))
PROPER(and(x0, __(z0, z1))) → c29(AND(proper(x0), __(proper(z0), proper(z1))), PROPER(x0), PROPER(__(z0, z1)))
PROPER(and(x0, and(z0, z1))) → c29(AND(proper(x0), and(proper(z0), proper(z1))), PROPER(x0), PROPER(and(z0, z1)))
PROPER(and(x0, isList(z0))) → c29(AND(proper(x0), isList(proper(z0))), PROPER(x0), PROPER(isList(z0)))
PROPER(and(x0, isNeList(z0))) → c29(AND(proper(x0), isNeList(proper(z0))), PROPER(x0), PROPER(isNeList(z0)))
PROPER(and(x0, isQid(z0))) → c29(AND(proper(x0), isQid(proper(z0))), PROPER(x0), PROPER(isQid(z0)))
PROPER(and(x0, isNePal(z0))) → c29(AND(proper(x0), isNePal(proper(z0))), PROPER(x0), PROPER(isNePal(z0)))
PROPER(and(x0, isPal(z0))) → c29(AND(proper(x0), isPal(proper(z0))), PROPER(x0), PROPER(isPal(z0)))
PROPER(and(__(z0, z1), x1)) → c29(AND(__(proper(z0), proper(z1)), proper(x1)), PROPER(__(z0, z1)), PROPER(x1))
PROPER(and(and(z0, z1), x1)) → c29(AND(and(proper(z0), proper(z1)), proper(x1)), PROPER(and(z0, z1)), PROPER(x1))
PROPER(and(isList(z0), x1)) → c29(AND(isList(proper(z0)), proper(x1)), PROPER(isList(z0)), PROPER(x1))
PROPER(and(isNeList(z0), x1)) → c29(AND(isNeList(proper(z0)), proper(x1)), PROPER(isNeList(z0)), PROPER(x1))
PROPER(and(isQid(z0), x1)) → c29(AND(isQid(proper(z0)), proper(x1)), PROPER(isQid(z0)), PROPER(x1))
PROPER(and(isNePal(z0), x1)) → c29(AND(isNePal(proper(z0)), proper(x1)), PROPER(isNePal(z0)), PROPER(x1))
PROPER(and(isPal(z0), x1)) → c29(AND(isPal(proper(z0)), proper(x1)), PROPER(isPal(z0)), PROPER(x1))
PROPER(and(x0, nil)) → c29(AND(proper(x0), ok(nil)), PROPER(x0))
PROPER(and(x0, tt)) → c29(AND(proper(x0), ok(tt)), PROPER(x0))
PROPER(and(x0, a)) → c29(AND(proper(x0), ok(a)), PROPER(x0))
PROPER(and(x0, e)) → c29(AND(proper(x0), ok(e)), PROPER(x0))
PROPER(and(x0, i)) → c29(AND(proper(x0), ok(i)), PROPER(x0))
PROPER(and(x0, o)) → c29(AND(proper(x0), ok(o)), PROPER(x0))
PROPER(and(x0, u)) → c29(AND(proper(x0), ok(u)), PROPER(x0))
PROPER(and(nil, x1)) → c29(AND(ok(nil), proper(x1)), PROPER(x1))
PROPER(and(tt, x1)) → c29(AND(ok(tt), proper(x1)), PROPER(x1))
PROPER(and(a, x1)) → c29(AND(ok(a), proper(x1)), PROPER(x1))
PROPER(and(e, x1)) → c29(AND(ok(e), proper(x1)), PROPER(x1))
PROPER(and(i, x1)) → c29(AND(ok(i), proper(x1)), PROPER(x1))
PROPER(and(o, x1)) → c29(AND(ok(o), proper(x1)), PROPER(x1))
PROPER(and(u, x1)) → c29(AND(ok(u), proper(x1)), PROPER(x1))
PROPER(isList(__(z0, z1))) → c31(ISLIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isList(and(z0, z1))) → c31(ISLIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isList(isList(z0))) → c31(ISLIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isList(isNeList(z0))) → c31(ISLIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isList(isQid(z0))) → c31(ISLIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isList(isNePal(z0))) → c31(ISLIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isList(isPal(z0))) → c31(ISLIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isList(nil)) → c31(ISLIST(ok(nil)))
PROPER(isList(tt)) → c31(ISLIST(ok(tt)))
PROPER(isList(a)) → c31(ISLIST(ok(a)))
PROPER(isList(e)) → c31(ISLIST(ok(e)))
PROPER(isList(i)) → c31(ISLIST(ok(i)))
PROPER(isList(o)) → c31(ISLIST(ok(o)))
PROPER(isList(u)) → c31(ISLIST(ok(u)))
PROPER(isNeList(__(z0, z1))) → c32(ISNELIST(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNeList(and(z0, z1))) → c32(ISNELIST(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNeList(isList(z0))) → c32(ISNELIST(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNeList(isNeList(z0))) → c32(ISNELIST(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNeList(isQid(z0))) → c32(ISNELIST(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNeList(isNePal(z0))) → c32(ISNELIST(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNeList(isPal(z0))) → c32(ISNELIST(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNeList(nil)) → c32(ISNELIST(ok(nil)))
PROPER(isNeList(tt)) → c32(ISNELIST(ok(tt)))
PROPER(isNeList(a)) → c32(ISNELIST(ok(a)))
PROPER(isNeList(e)) → c32(ISNELIST(ok(e)))
PROPER(isNeList(i)) → c32(ISNELIST(ok(i)))
PROPER(isNeList(o)) → c32(ISNELIST(ok(o)))
PROPER(isNeList(u)) → c32(ISNELIST(ok(u)))
PROPER(isQid(__(z0, z1))) → c33(ISQID(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isQid(and(z0, z1))) → c33(ISQID(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isQid(isList(z0))) → c33(ISQID(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isQid(isNeList(z0))) → c33(ISQID(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isQid(isQid(z0))) → c33(ISQID(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isQid(isNePal(z0))) → c33(ISQID(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isQid(isPal(z0))) → c33(ISQID(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isQid(nil)) → c33(ISQID(ok(nil)))
PROPER(isQid(tt)) → c33(ISQID(ok(tt)))
PROPER(isQid(a)) → c33(ISQID(ok(a)))
PROPER(isQid(e)) → c33(ISQID(ok(e)))
PROPER(isQid(i)) → c33(ISQID(ok(i)))
PROPER(isQid(o)) → c33(ISQID(ok(o)))
PROPER(isQid(u)) → c33(ISQID(ok(u)))
PROPER(isNePal(__(z0, z1))) → c34(ISNEPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isNePal(and(z0, z1))) → c34(ISNEPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isNePal(isList(z0))) → c34(ISNEPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isNePal(isNeList(z0))) → c34(ISNEPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isNePal(isQid(z0))) → c34(ISNEPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isNePal(isNePal(z0))) → c34(ISNEPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isNePal(isPal(z0))) → c34(ISNEPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isNePal(nil)) → c34(ISNEPAL(ok(nil)))
PROPER(isNePal(tt)) → c34(ISNEPAL(ok(tt)))
PROPER(isNePal(a)) → c34(ISNEPAL(ok(a)))
PROPER(isNePal(e)) → c34(ISNEPAL(ok(e)))
PROPER(isNePal(i)) → c34(ISNEPAL(ok(i)))
PROPER(isNePal(o)) → c34(ISNEPAL(ok(o)))
PROPER(isNePal(u)) → c34(ISNEPAL(ok(u)))
PROPER(isPal(__(z0, z1))) → c35(ISPAL(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
PROPER(isPal(and(z0, z1))) → c35(ISPAL(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
PROPER(isPal(isList(z0))) → c35(ISPAL(isList(proper(z0))), PROPER(isList(z0)))
PROPER(isPal(isNeList(z0))) → c35(ISPAL(isNeList(proper(z0))), PROPER(isNeList(z0)))
PROPER(isPal(isQid(z0))) → c35(ISPAL(isQid(proper(z0))), PROPER(isQid(z0)))
PROPER(isPal(isNePal(z0))) → c35(ISPAL(isNePal(proper(z0))), PROPER(isNePal(z0)))
PROPER(isPal(isPal(z0))) → c35(ISPAL(isPal(proper(z0))), PROPER(isPal(z0)))
PROPER(isPal(nil)) → c35(ISPAL(ok(nil)))
PROPER(isPal(tt)) → c35(ISPAL(ok(tt)))
PROPER(isPal(a)) → c35(ISPAL(ok(a)))
PROPER(isPal(e)) → c35(ISPAL(ok(e)))
PROPER(isPal(i)) → c35(ISPAL(ok(i)))
PROPER(isPal(o)) → c35(ISPAL(ok(o)))
PROPER(isPal(u)) → c35(ISPAL(ok(u)))
TOP(mark(__(z0, z1))) → c46(TOP(__(proper(z0), proper(z1))), PROPER(__(z0, z1)))
TOP(mark(and(z0, z1))) → c46(TOP(and(proper(z0), proper(z1))), PROPER(and(z0, z1)))
TOP(mark(isList(z0))) → c46(TOP(isList(proper(z0))), PROPER(isList(z0)))
TOP(mark(isNeList(z0))) → c46(TOP(isNeList(proper(z0))), PROPER(isNeList(z0)))
TOP(mark(isQid(z0))) → c46(TOP(isQid(proper(z0))), PROPER(isQid(z0)))
TOP(mark(isNePal(z0))) → c46(TOP(isNePal(proper(z0))), PROPER(isNePal(z0)))
TOP(mark(isPal(z0))) → c46(TOP(isPal(proper(z0))), PROPER(isPal(z0)))
TOP(ok(__(__(z0, z1), z2))) → c47(TOP(mark(__(z0, __(z1, z2)))), ACTIVE(__(__(z0, z1), z2)))
TOP(ok(__(z0, nil))) → c47(TOP(mark(z0)), ACTIVE(__(z0, nil)))
TOP(ok(__(nil, z0))) → c47(TOP(mark(z0)), ACTIVE(__(nil, z0)))
TOP(ok(and(tt, z0))) → c47(TOP(mark(z0)), ACTIVE(and(tt, z0)))
TOP(ok(isList(z0))) → c47(TOP(mark(isNeList(z0))), ACTIVE(isList(z0)))
TOP(ok(isList(nil))) → c47(TOP(mark(tt)), ACTIVE(isList(nil)))
TOP(ok(isList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isList(z1)))), ACTIVE(isList(__(z0, z1))))
TOP(ok(isNeList(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNeList(z0)))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isList(z0), isNeList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNeList(__(z0, z1)))) → c47(TOP(mark(and(isNeList(z0), isList(z1)))), ACTIVE(isNeList(__(z0, z1))))
TOP(ok(isNePal(z0))) → c47(TOP(mark(isQid(z0))), ACTIVE(isNePal(z0)))
TOP(ok(isNePal(__(z0, __(z1, z0))))) → c47(TOP(mark(and(isQid(z0), isPal(z1)))), ACTIVE(isNePal(__(z0, __(z1, z0)))))
TOP(ok(isPal(z0))) → c47(TOP(mark(isNePal(z0))), ACTIVE(isPal(z0)))
TOP(ok(isPal(nil))) → c47(TOP(mark(tt)), ACTIVE(isPal(nil)))
TOP(ok(isQid(a))) → c47(TOP(mark(tt)), ACTIVE(isQid(a)))
TOP(ok(isQid(e))) → c47(TOP(mark(tt)), ACTIVE(isQid(e)))
TOP(ok(isQid(i))) → c47(TOP(mark(tt)), ACTIVE(isQid(i)))
TOP(ok(isQid(o))) → c47(TOP(mark(tt)), ACTIVE(isQid(o)))
TOP(ok(isQid(u))) → c47(TOP(mark(tt)), ACTIVE(isQid(u)))
TOP(ok(__(z0, z1))) → c47(TOP(__(active(z0), z1)), ACTIVE(__(z0, z1)))
TOP(ok(__(z0, z1))) → c47(TOP(__(z0, active(z1))), ACTIVE(__(z0, z1)))
TOP(ok(and(z0, z1))) → c47(TOP(and(active(z0), z1)), ACTIVE(and(z0, z1)))

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:none
Defined Rule Symbols:

active, __, and, isList, isNeList, isQid, isPal, proper, isNePal

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

(55) CdtUsableRulesProof (EQUIVALENT transformation)

The following rules are not usable and were removed:

active(__(__(z0, z1), z2)) → mark(__(z0, __(z1, z2)))
active(__(z0, nil)) → mark(z0)
active(__(nil, z0)) → mark(z0)
active(and(tt, z0)) → mark(z0)
active(isList(z0)) → mark(isNeList(z0))
active(isList(nil)) → mark(tt)
active(isList(__(z0, z1))) → mark(and(isList(z0), isList(z1)))
active(isNeList(z0)) → mark(isQid(z0))
active(isNeList(__(z0, z1))) → mark(and(isList(z0), isNeList(z1)))
active(isNeList(__(z0, z1))) → mark(and(isNeList(z0), isList(z1)))
active(isNePal(z0)) → mark(isQid(z0))
active(isNePal(__(z0, __(z1, z0)))) → mark(and(isQid(z0), isPal(z1)))
active(isPal(z0)) → mark(isNePal(z0))
active(isPal(nil)) → mark(tt)
active(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(__(z0, z1)) → __(active(z0), z1)
active(__(z0, z1)) → __(z0, active(z1))
active(and(z0, z1)) → and(active(z0), z1)
__(z0, mark(z1)) → mark(__(z0, z1))
__(ok(z0), ok(z1)) → ok(__(z0, z1))
__(mark(z0), z1) → mark(__(z0, z1))
and(mark(z0), z1) → mark(and(z0, z1))
and(ok(z0), ok(z1)) → ok(and(z0, z1))
isList(ok(z0)) → ok(isList(z0))
isNeList(ok(z0)) → ok(isNeList(z0))
isQid(ok(z0)) → ok(isQid(z0))
isPal(ok(z0)) → ok(isPal(z0))
proper(__(z0, z1)) → __(proper(z0), proper(z1))
proper(nil) → ok(nil)
proper(and(z0, z1)) → and(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(isList(z0)) → isList(proper(z0))
proper(isNeList(z0)) → isNeList(proper(z0))
proper(isQid(z0)) → isQid(proper(z0))
proper(isNePal(z0)) → isNePal(proper(z0))
proper(isPal(z0)) → isPal(proper(z0))
proper(a) → ok(a)
proper(e) → ok(e)
proper(i) → ok(i)
proper(o) → ok(o)
proper(u) → ok(u)
isNePal(ok(z0)) → ok(isNePal(z0))

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = 0
POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(__'(x₁, x₂)) = [4]x₁ + [2]x₂
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = [4] + x₁
POL(ok(x₁)) = x₁

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

AND(ok(z0), ok(z1)) → c26(AND(z0, z1))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = [4]x₂
POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = 0
POL(ok(x₁)) = [2] + x₁

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

AND(mark(z0), z1) → c25(AND(z0, z1))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = [4]x₁ + [4]x₂
POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = [3]x₁
POL(ISNEPAL(x₁)) = [5]x₁
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = x₁
POL(__'(x₁, x₂)) = [3]x₁
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = [2] + x₁
POL(ok(x₁)) = x₁

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = [3]x₁
POL(ISLIST(x₁)) = x₁
POL(ISNELIST(x₁)) = [2]x₁
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = x₁
POL(ok(x₁)) = [2] + x₁

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = [4]x₂
POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = [3]x₁
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = 0
POL(__'(x₁, x₂)) = x₂
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = x₁
POL(ok(x₁)) = [2] + x₁

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

ISQID(ok(z0)) → c43(ISQID(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

ISPAL(ok(z0)) → c45(ISPAL(z0))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = 0
POL(ISLIST(x₁)) = [2]x₁
POL(ISNELIST(x₁)) = [4]x₁
POL(ISNEPAL(x₁)) = [2]x₁
POL(ISPAL(x₁)) = [2]x₁
POL(ISQID(x₁)) = 0
POL(__'(x₁, x₂)) = 0
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = 0
POL(ok(x₁)) = [2] + x₁

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:

ISQID(ok(z0)) → c43(ISQID(z0))

K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

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

ISQID(ok(z0)) → c43(ISQID(z0))

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

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

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

POL(AND(x₁, x₂)) = [3]x₂
POL(ISLIST(x₁)) = 0
POL(ISNELIST(x₁)) = 0
POL(ISNEPAL(x₁)) = 0
POL(ISPAL(x₁)) = 0
POL(ISQID(x₁)) = [4]x₁
POL(__'(x₁, x₂)) = 0
POL(c22(x₁)) = x₁
POL(c23(x₁)) = x₁
POL(c24(x₁)) = x₁
POL(c25(x₁)) = x₁
POL(c26(x₁)) = x₁
POL(c41(x₁)) = x₁
POL(c42(x₁)) = x₁
POL(c43(x₁)) = x₁
POL(c44(x₁)) = x₁
POL(c45(x₁)) = x₁
POL(mark(x₁)) = 0
POL(ok(x₁)) = [1] + x₁

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
ISQID(ok(z0)) → c43(ISQID(z0))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))

S tuples:none
K tuples:

__'(mark(z0), z1) → c22(__'(z0, z1))
__'(z0, mark(z1)) → c23(__'(z0, z1))
AND(ok(z0), ok(z1)) → c26(AND(z0, z1))
AND(mark(z0), z1) → c25(AND(z0, z1))
ISLIST(ok(z0)) → c41(ISLIST(z0))
ISNELIST(ok(z0)) → c42(ISNELIST(z0))
__'(ok(z0), ok(z1)) → c24(__'(z0, z1))
ISNEPAL(ok(z0)) → c44(ISNEPAL(z0))
ISPAL(ok(z0)) → c45(ISPAL(z0))
ISQID(ok(z0)) → c43(ISQID(z0))

Defined Rule Symbols:none

Defined Pair Symbols:

__', AND, ISLIST, ISNELIST, ISQID, ISNEPAL, ISPAL

Compound Symbols:

c22, c23, c24, c25, c26, c41, c42, c43, c44, c45

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

The set S is empty

(0) Obligation:

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

(2) Obligation:

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

(4) Obligation:

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

(6) Obligation:

(7) CdtUsableRulesProof (EQUIVALENT transformation)

(8) Obligation:

(9) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)

(10) Obligation:

(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(12) Obligation:

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

(14) Obligation:

(15) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

(16) Obligation:

(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(18) Obligation:

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

(20) Obligation:

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(22) Obligation:

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

(24) Obligation:

(25) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(26) Obligation:

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

(28) Obligation:

(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(30) Obligation:

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

(32) Obligation:

(33) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(34) Obligation:

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

(36) Obligation:

(37) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(38) Obligation:

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

(40) Obligation:

(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(42) Obligation:

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

(44) Obligation:

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(46) Obligation:

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

(48) Obligation:

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

(50) Obligation:

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

(52) Obligation:

(53) CdtUnreachableProof (EQUIVALENT transformation)

(54) Obligation:

(55) CdtUsableRulesProof (EQUIVALENT transformation)

(56) Obligation:

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

(58) Obligation:

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

(60) Obligation:

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

(62) Obligation:

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

(64) Obligation:

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

(66) Obligation:

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

(68) Obligation:

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

(70) Obligation:

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

(72) BOUNDS(O(1), O(1))